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Inductiue  Series, 


FIRST    LESSONS 


AEITHMETIC 


INDUCTIVE    PLAN, 


INCLUDING 


ORAL  AND  WRITTEN  EXERCISES. 


BY 


WILLIAM  J^MILNE,  A.M. 

PRINCIPAL  OF   TiJJ(e(^^£~NORS^£^SieftpOI.,   GENESEO,   N.  Y. 


JONES  BROTHERS  &  COMPANY: 


CINCINNATI,  PHILADELPHIA, 

CHICAGO,  MEMPHIS. 

1878. 


COPYKIGHT,    1878,    BY   JOHN   T.  JONES. 


ELECTROTYPED  AT 

FRANKLIN  TYl'E  KOUNDRY, 

CINCINNATI. 


This  book  is  designed  to  teach  the  principles  of  Arithmetical 
Science  as  far  as  they  are  involved  in  the  elementary  processes,  and 
to  secure  a  reasonable  degree  of  accuracy  and  rapidity  in  express- 
ing numbers  and  computing  results. 

The  pupils  for  whose  use  this  book  is  intended  can  not  be  ex- 
pected, at  the  outset,  to  explain  processes,  give  definitions,  or  assign 
reasons,  though  their  notions  of  all  of  them  may  be  quite  correct; 
much  less  should  they  be  expected  to  grasp  the  principles  of  a 
science  by  committing  to  memory  statements  which  are  the  deduc- 
tions and  generalizations  of  persons  entirely  familiar  with  the  sub- 
jects treated.  And,  therefore,  this  work  has  been  prepared  upon  the 
inductive  and  objective  methods,  so  that  the  pupil  may  obtain  his 
knowledge  of  arithmetic  from  actual  work  with  numbers,  rather 
than  from  the  stereotyped  statements  of  the  book. 

The  true  method  of  awakening  in  the  child  a  clear  idea  of  num- 
bers is  through  a  perception  of  objects,  or  by  pictures  or  other  repre- 
sentations of  them.  After  he  has  become  familiar  with  things  and 
their  names,  the  name  will  signify  to  him  all  that  he  needs  to  know 
about  the  objects  so  far  as  number  is  concerned;  and  it  is  no  longer 
necessary  that  the  objects  should  be  present  before  him.  The  ne- 
cessity, too,  of  associating  the  same  numbers  with  such  a  variety 
of  things,  causes  him  at  length  to  cease  to  regard  them  in  connec- 
tion with  any  particular  thing,  or  as  any  thing  more  than  abstrac- 
tions. 

(iii) 


IV  P  K  E  F  A  C  E  . 

In  harmony  with  these  laws  of  the  development  and  growth  of 
mind,  this  work  presents  at  first  the  idea  of  number  connected  with 
visual  representations  of  objects;  afterward,  when  the  pupils  become 
familiar  with  the  objects,  concrete  examples  are  given  without  illus- 
tration, and  these  are  immediately  followed  by  exercises  upon  ab- 
stract numbers,  so  that  the  pupil  may  become  familiar  with  the 
various  combinations  that  may  be  formed.* 

The  first  lessons  are  devoted  to  instruction  in  counting,  reading, 
and  writing  numbers  up  to  twenty.  Immediately  following  these, 
are  lessons  upon  Addition,  in  which  abundant  practice  is  given  in 
combining  numbers.  The  fundamental  processes  of  Subtraction, 
Multiplication  and  Division,  are  treated  upon  a  plan  similar  to 
that  exemplified  in  Addition,  including  besides,  numerous  ex- 
amples combining  two  or  more  of  the  previous  processes. 

The  lessons  on  Fractions  are  so  simple  and  yet  so  thorough,  that 
the  pupil  is  enabled  to  read,  write,  add,  subtract,  multiply,  and 
divide  fractions  when  the  processes  are  not  very  complex. 

The  work  on  Written  Arithmetic,  which  follows,  is  believed  to  be 
simple,  thorough,  and  practical;  and  the  brief  and  practical  treat- 
ment of  the  various  classes  of  denominate  numbers  in  common  use, 
makes  the  work  quite  comprehensive  within  its  scope. 

With  the  hope  that  the  features  of  this  book  will  commend  it  to 
all  intelligent  persons,  and  that  instruction  in  the  rudiments  of 
arithmetic  may  be  rendered  more  interesting  and  efiective  through 
its  agency,  it  is  confidently  offered  to  the  public. 

W.  J.  M. 

State  Normal  School, 

Geneseo,  N.  Y.,  Januciry,  1878. 


i 


CONTENTSI 


^1 


7^\ 


I.  Objects  and  numbers  from  1  to  10  . 
II.  Counting  numbers  from  1  to  20 

III.  Oral  and  slate  exercises  in  Addition 

IV.  Special  review  of  Addition 
V.  Oral  and  slate  exercises  in  Subtraction 

VI.  Special  review  of  Subtraction  and  Addition 
VII.  Heading  and  writing  numbers  to  100     . 
VIII.  Oral  and  slate  exercises  in  Multiplication 

IX.  Special    review   of    Multiplication,    Subtraction 

Addition 

X.  Oral  and  slate  exercises  in  Division 
XI.  Special  review  of    Division,   Multiplication 

tion,  and  Addition       .... 
XII.  Heading  and  writing  Fractions 

XIII.  Addition  of  Simple  Fractions 

XIV.  Subtraction  of  Simple  Fractions     . 
XV.  Multiplication  of  Simple  Fractions 

XVI.  Division  of  Simple  Fractions 
XVII.  Notation  and  Numeration  of  Numbers  . 
XVIII.  Written  exercises  in  Addition 
XIX.  Written  exercises  in  Subtraction     . 
XX.  Written  exercises  in  Multiplication 
XXI.  Written  exercises  in  Division 
XXII.  Exercises  in  Denominate  Numbers 
XXIII.  Table  of  Boman  Notation 


Subtrac- 


and 


16 
30 
32 
48 
50 
53 

70 

72 

91 

93 

96 

99 

103 

104 

107 

113 

118 

122 

128 

134 

144 


(V) 


Jhe  Inductive  ^£rie^ 

OF 

MATHEMATICAL  TEXT-BOOKS. 


I.  FIRST  LESSONS  IN  ARITHMETIC. 

II.  PRACTICAL  ARITHMETIC. 

III.  KET  TO  PRACTICAL  ARITHMETIC. 

IV.  ELEMENTS  OF  ALGEBRA.     {In  preparation.-) 
V.  ELEMENTS  OF  GEOMETRY.     {In  preparation.) 


(vi) 


«*  > 


FIRST   LESSOtI£BflVBB.»IT 


ilPOT^ 


t^i 


Jv    -A"   7<-  yi>   ^ 


1 


NUMBERS  FRmi^  TO  10 


■t- 


Dog 


One 

Two       Trees  2 

Three  Horses  3 

Four    Sheep  4 

Five     Houses  5 


I. 

II. 

III. 

IV. 

V. 


Sloe       Ships        6  VI. 

Seven  Birds        7  A^II. 

J5J/r//if  Books       8  VIII, 

Nine     Cherries    9  IX. 

Ten       Stars      10  X. 

,.  -(vii) 


8 


FIRST    LESSONS 


liESSOlS^   I. 

1.  Of  what  is  this  a  picture? 

2.  How  many  tables  are  there  in  the  picture? 

3.  How  many  balls  are  there? 

4.  Make  as  many  marks  on  your  slates  as  there 
are  lamps  in  the  picture. 

5.  The  figure  1  represents  one  table,  one  ball,  one 
lamp,  or  one  object  of  any  kind. 

6.  Make  the  figure  one  on  your  slates.    /. 

7.  How  many  kittens  are  playing  with  the  ball? 

8.  How  many  kittens  are  playing  with  the  cat? 

9.  How  many  kittens  are  1  kitten  and  1  kitten? 

10.  How  many  chairs  do  you  see  in  the  picture? 

11.  Name  two  objects  on  the  table. 

12.  Make  two  marks  on  your  slates. 

13.  The  figure  2  represents  two  chairs,  two  books, 
or  two  objects  of  any  kind. 

14.  Make  the  figure  two  on  your  slates.    ^. 

15.  Make  the  figures  one  and  two. 


IN    ARITHMETIC. 


LESSON  II. 

1.  How  many  boats  do  you  see  in  the  picture? 

2.  How  many  fishes  has  one  of  the  boys  caught? 

3.  How  many  fishes  has  the  other  boy  caught? 

4.  Two  fishes  and  one  fish  are  how  many  fishes? 

5.  How  many  fishing-rods  do  you  see? 

6.  Make  as  many  marks  as  there  are  fishing-rods. 

7.  The  figure  3  represents  three  objects. 

8.  Make  the  figure  three  on  your  slates.    */. 

9.  Make  the  figures  one,  two  and  three. 

10.  How  many  boys  in  the  picture  are  fishing? 

11.  How  many  boys  are  digging  for  bait? 

12.  How  many  boys  are  three  boys  and  one  boy? 

13.  How  many  oars  has  each  boat  in  the  picture? 

14.  Make  as  many  marks  on   your  slates  as  there 
are  boys  in  the  picture. 

15.  The  figure  4  represents  four  objects. 

16.  Make  the  figure  four  on  your  slates.    ^. 

17.  Make  the  figures  one,  two,  three  and  four. 


10 


FIRST    LESSONS 


LESSOI^    III. 

1.  How  many  roses  do  you  see  on  the  bush? 

2.  How  many  birds  are  flying  near  the  bush? 

3.  How  many  birds  are  there  on  the  bush  ? 

4.  How  many  birds  are  four  birds  and  one  bird? 

5.  How  many  eggs  are  there  in  the  nest? 

6.  Make  a  mark  for  every  egg  in  the  nest. 

7.  The  figure  5  represents  five  things. 

8.  Make  the  figure  five  on  your  slates.    <^, 

9.  Make  the  figures  one,  two,  three,  four  and  five. 

10.  How  many  rose-buds  are  there  near  each  other? 

11.  How  many  do  you  find  growing  alone? 

12.  How  many  rose-buds  are  five  rose-buds  and  one 
rose-bud  ? 

13.  Make  six  marks  on  your  slates. 

14.  The  figure  6  represents  six  things. 

15.  Make  the  figure  six  on  your  slates.    ^ 

16.  Make  the  figures  one,  two,  three,  four,  five,  six. 

/       J       J       J        ^       ^ 


IN    ARITHMETIC, 


11 


I^ESSON^    IV. 

1.  How  many  lambs  are  at  the  left  in  the  picture? 

2.  How  many  trees  are  in  a  row  in  the  picture? 

3.  How  many  trees  are  standing  alone? 

4.  How  many  trees  are  six  trees  and  one  tree? 

5.  How  many  lambs  are  there  in  the  picture? 

6.  Make  seven  marks  on  your  slates. 

7.  The  figure  7  represents  seven  things. 

8.  Make  the  figure  seven  on  your  slates.    /^ 

9.  How  many  sheep  are  feeding  in  the  field? 

10.  How  many  sheep  are  with  the  lambs? 

11.  Seven  sheep  and  one  sheep  are  how  many  sheep? 

12.  How  many  posts  do  you  see  in  the  picture? 

13.  Make  as  many  marks  as  there  are  posts. 

14.  The  figure  8  represents  eight  things. 

15.  Make  the  figure  eight  on  your  slates.      <f. 

16.  Make  the  figures  one,  two,  three,  four,  five,  six, 
seven,  eight. 


12 


FIKST    LESSONS 


liESSON    V. 


1.  How  many  trees   are  there   in   a   row  in   the 
picture  ? 

2.  On  how  many  trees  are  there  ladders? 

3.  How  many  trees  are  eight  trees  and  one  tree? 

4.  How  many  rounds  has  the  ladder? 

5.  Make  nine  marks  on  your  slates. 

6.  The  figure  9  represents   nine    objects  of  any 
kind. 

7.  Make  the  figure  nine  on  your  slates.    ^' 

8.  How  many  loads  of  grain  are  there? 

9.  How  many  horses  do  you  see? 

10.  How  many  rakes  are  there  in  the  picture? 

11.  How  many  rails  are  there  in  each  section  of 
fence  in  the  picture? 

12.  How  many  men  do  you  see  in  the  picture? 

13.  How  many  shocks  of  grain  are  there? 

14.  How  many  sections  of  fence  are  there? 

15.  How  many  posts  has  the  fence? 

16.  Make  the  nine  figures  on  your  slates. 

/      J       J      J        ^      ^      /      . 


/ 


IN    ARITHMETIC, 


13 


liESSOI^   TI. 


How  many 


1.  How  many  cherries   are  there  on   the  larger 
twig  in  the  picture? 

2.  How  many  cherries 
are  on  the  other  twig? 

3.  How  many  cherries 
are  nine  cherries  and  one 
cherry?     Ten  cherries. 

4.  Make  nine  marks  and  one  mark, 
marks  are  nine  marks  and  one  mark  ? 

5.  How  many  pens  are  nine  pens  and  one  pen  ? 

6.  How  many  boys  are  nine  boys  and  one  boy? 

7.  How  many  pears  are  there  represented  in  the 
following  picture? 

8.  How  many  groups 
of  ten  pears  are  there? 

9.  Make  ten  straight 
marks  on  your  slates. 

10.  The  number  ten  is 
expressed  thus:   10, 

11.  The  figure  1  at  the  left  shows  that  there  is  one 
ten.  The  figure  0  at  the  right  shows  that  there  are 
no  ones, 

12.  Express  ten.  What  does  the  figure  1  denote? 
What  does  the  figure  0  denote? 

13.  How  many  fingers  have  you  on  both  hands? 

14.  Make  as  many  marks  as  you  have  fingers. 

15.  Express  the  number  ten  by  figures. 

16.  Name  ten  things  that  you  see. 


#^ 


14 


FIRST    LESSONS 


LESSON    Til. 

1.  How  many  ducks  are  swimming  in  the  pond? 

2.  How  many  ducks  are  there  on  the  bank? 

3.  Ten  ducks 
and  one  duck 
are  how  many? 
Eleven  ducks. 

4.  How  many 
groups  of  ten 
ducks  are  there? 

5.  How  many 
ducks  are  there  besides  the  group  of  ten  ducks? 

6.  Make  ten  marks  and  one  mark.      (//////////]  / 

7.  Eleven  is  expressed  thus :  11* 

8.  Express  eleven  on  your  slates. 

When  tivo  figures  are  written  side  by  side,  the  one  on 
the  right  denotes  ones,  the  one  next  to  it  denotes  tens. 

9.  Express  ten.     Express  eleven.     What  does  10 
represent?     What  does  11  represent? 

10.  Make  ten  marks  in  a  group  and  two  besides 
on  your  slates.  (//////////)  // 

11.  How    many    marks    are    ten    marks    and    two 
marks?     Twelve  marks. 

12.  Express  one  ten  and  two  ones,  or  twelve.     12, 

13.  Express  with  figures,  ten,  eleven  and  twelve. 

14.  Make  ten  marks  and  three  marks.  (//////////J  /// 

15.  Ten  and  three,  or  thirteen,  is  expressed  thus :  13, 

16.  Write  all  the  numbers  from  one  to  thirteen. 


i:n   arithmetic.  15 

liESSON  VIII. 

1.  Make  ten  marks  and  four  marks,  or  fourteen 
marks,  on  your  slates.  [llllllllll]  I  III 

2.  Fourteen  is  expressed  thus :   14=. 

3.  How  many  books  are  ten  books  and  four  books? 

4.  Represent  ten  books  and  five  books,  or  fifteen 
books,  by  marks.  [llllllllll]  lllll 

5.  Express  one  ten  and  five  ones,  or  fifteen.     15» 

6.  How  many  are  one  ten  and  six  ones? 

7.  Express  one  ten  and  six  ones,  or  sixteen.     10. 

8.  Express  one  ten  and  seven  ones,  or  seventeen.  17* 

9.  Express  eighteen.    18.      Express  nineteen,    10. 

10.  Make  ten    marks   and  ten   marks   in    separate 
groups  on  your  slates.  [llllllllll)  [llllllllll) 

11.  How  many  tens  are  one  ten  and  one  ten? 

12.  Express  two  tens,  or  tioenty.     20, 

13.  What  does  0  denote?     What  does  2  denote? 

14.  Express  by  figures  all  the  numbers  from  one 
to  twenty. 

15.  How  many  tens  are  there  in  fifteen? 

16.  How  many  ones  are  there  in  fifteen? 

17.  How  many  tens  are  there  in  twenty-four? 

18.  How  many  ones  are  there  in  twenty-four? 

19.  What  shows  that  there  are  no  ones  in  a  number? 

Slate  Exercises. 
Copy  and  read  the  following : 

12  11  10  19     ^y^^^ 

16  13  14  17  ^^5oe  T'lR 


16 


FIRST    LESSONS 


liESSON    IX. 

1.  How  many  balls  are  1  ball  and  2  balls?     Ex- 
press the  answer  on  your  slates,  thus:   1  ball  and  2 

balls   are  3   balls;   or,   1 
and  2  are  3. 

2.  How  many  balls 
are  2  balls  and  2  balls? 
Express  the  answer  thus  : 

2  balls  and  2  balls  are  4 
balls;  or,  2  and  2  are  4. 

3.  How  many  balls 
are  3  balls  and  2  balls? 
Express  the  answer  thus : 

3  balls  and  2  balls  are  5 
3  +  2  =  5. 

It 


balls;  or,  3  and  2  are  5. 


The  sign  +  takes  the  place  of  the  word  and 
is  read  jplus. 

The  sign  =  takes  the  place  of  the  word  are.  It 
is  read  equal.  Then  1  and  2  are  3,  is  written  1  +  2 
=  3,  and  read,  1  plus  2  equal  3. 

4.  Express  2  and  2  are  4,  and  3  and  2  are  5,  on 
your  slates,  using  the  signs. 

5.  How  many  balls  are  4  balls  and  2  balls? 
4+2=?    5+2=?    6+2=?    7+2=?     8+2=? 

6.  How  many  are  9  balls  and  2  balls?     10  +  2  =  ? 

Counting  numbers  together  is  called  Addition* 

7.  Form  the  addition  table  of  twos. 


IN     ARITHMETIC, 
TABLE. 


17 


1  +  2  =  3 

4+2  =  6 

7  +  2=    9 

2  +  2  =  4 

5  +  2  =  7 

8+2  =  10 

3  +  2  =  5 

6  +  2  =  8 

9  +  2  =  11 

Slate  Exeecises. 

Copy  and  add  the  following : 

242728623 
629252242 


:>J<Kc 


1.  How  many  birds  are  1  bird  and  3  birds? 

2.  How  many  acorns  are  2  acorns  and  3  acorns? 

3.  Harry  bought  3 
oranges  one  day,  and  3      i^iTw^J^  A 
the   next.     How  many         ^s     ^?^*^^ 
oranges  did  he  buy? 

4.  How    many    figs 
are  4  figs  and  3  figs? 

5.  How  many  boys 
are  5  boys  and  3  boys? 

6.  Helen  gave  a  beggar  6  cents,  and  Mary  gave 
him  3  cents.     How  many  cents  did  both  give  him? 

7.  A  man  bought  7  loads  of  hay  one  week,   and 
3  the  next.     How  many  loads  of  hay  did  he  buy? 

2 


18 


FIEST    LESSONS 


8.  How  many  are    8   and   3?     How  many  are   9 
and  3? 

9.  How  many  tops  are  10  tops  and  3  tops? 

10.  How  many  bees  are  1  bee  and  4  bees? 

11.  How  many  butterflies  are  2  butterflies  and  4 
butterflies  ? 

12.  Mary  had  3  cents,  and  her  brother  gave  her 
4  more.     How  many  cents  had  she  then? 

13.  A'  boy  bought   4  pencils   one  day,  and  4  the 
next.     How  many  pencils  did  he  buy  in  both  days? 

14.  How  many  books  are   5  books   and  4  books? 

15.  How  many  are  6  and  4?      7  and  4? 

16.  If  there   are   7   boys   on   one   seat  and   4   on 
another,  how  many  boys  are  there  on  both  seats? 

17.  8  +  4  =  ?     9  +  4  =  ?     10  +  4  =  ? 

18.  Form  the  tables  of  threes  and  fours. 

TABLES. 


1+3=4      6+3=   9 

1+4  =  5      6  +  4  =  10 

2  +  3  =  5      7  +  3  =  10 

2  +  4  =  6      7  +  4  =  11 

3  +  3  =  6      8  +  3=11 

3  +  4=7      8  +  4  =  12 

4  +  3  =  7      9  +  3  =  12 

4  +  4  =  8      9  +  4=13 

5  +  3  =  8    10  +  3  =  13 

5  +  4=9    10  +  4  =  14 

Slate  Exercises. 

Copy  and  add  the  following: 

3473434526 
52495822   73 


IN    ARITHMETIC.  19 


I.ES80N   XI. 


1.  James    had    3   oranges,    and    bought   4   more. 
How  many  had  he  then  ?     3  -f  4  =  ? 

2.  Mary  had  4  pencils,  and  her  aunt  gave  her  2 
more.     How  many  had  she  then? 

3.  If  there   are    9   cows    in   one   field   and   3   in 
another,  how  many  are  there  in  both  fields? 

4.  John   had  4   pennies,    and    earned    7   pennies. 
How  many  had  he  then? 

5.  Helen  picked  3  roses  from  one  bush  and  7  from 
another.     How  many  roses  did  she  pick  from  both? 

6.  One  hen's  nest  had   3  eggs  in  it,  and  another 
had  5.     How  many  eggs  were  there  in  both  nests? 

7.  3  +  4  =  ?     4  +  7==?     4  +  6  =  ? 

8.  There  are  6  lambs  in  one  field  and  2  in  another. 
How  many  lambs  in  both  fields?     6  +  2  =  ? 

9.  4  +  2  =  ?     7  +  3  =  ?    3  +  5  =  ? 

10.  A  man  paid  10  dollars  for  a  coat  and  4  dol- 
lars for  a  hat.     What  did  he  pay  for  both? 

11.  9  +  3  =  ?     3  +  8  =  ?     8  +  4  =  ? 

12.  How  many  are  10  and  2?     2  and  10? 

13.  How  many  are  9  and  2?     2  and  9? 

14.  How  many  robins  are  5  robins  and  3  robins? 

Slate  Exercises. 

Copy  and  add  the  following: 

3865897621 
7434224318 


20 


FIEST    LESSONS 


liESSOlS^    XII. 

1.  There  is  1  pigeon  on  one  lirab  and  there  are  5 
pigeons   on   another.     How  many  are  there   on  both 

limbs?     1  +  5  =  ? 
^'^  2.  A    man    put    2 

bushels  of  wheat  in 
one  bin  and  5  in 
another.  How  many 
bushels  did  he  put  in 
both  bins?  2  +  5  =  ? 
3.  Richard  gave  3 
cents  for  a  lemon  and  5  cents  for  an  orange.  How 
much  did  he  give  for  both  ?    3  +  5  =  ? 

4.  How  many  girls  are  4  girls  and  5  girls? 

5.  How  many  canes  are  5  canes  and  5  canes? 

6.  6  +  5  =  ?     7  +  5  =  ?     8  +  5  =  ?     9  +  5  =  ? 

7.  How  many  sheep  are  10  sheep  and  5  sheep? 

8.  A  girl  gave  1  cent  for  a  needle  and  6  cents 
for  a  spool  of  thread.  How  much  did  she  pay  for 
both?     1  +  6  =  ? 

9.  A  boy  gave  2  cents  for  marbles  and  6  cents 
for  a  top.     How  much  did  he  pay  for  both? 

10.  How  many  lamps  are  3  lamps  and  6  lamps? 

11.  How  many  are  4  and  6?  How  many  are  5 
and  6? 

12.  A  man  bought  6  bushels  of  potatoes  at  one 
time,  and  6  more  at  another  time.  How  many  did 
he  buy  at  both  purchases  ?      6  -{-  Q^^'} 

13.  How  many  lambs  are  7  lambs  and  6  lambs? 


IN    ARITHMETIC. 


21 


14.  How  many  are  8   and   6?      How  many  are   9 
and  6? 

15.  How  many  pinks  are  10  pinks  and  6  pinks? 

16.  Form  addition  tables  of  fives  and  sixes. 

TABLES. 


1  +  5-=  6  6  +  5-=ll 

1  +  6=  7  6  +  6  =  12 

2  +  5=  7  7  +  5  =  12 

2  +  6=  8  7  +  6  =  13 

3  +  5=  8  8  +  5  =  13 

3  +  6=  9  8  +  6  =  14 

4  +  5=  9   9  +  5  =  14 

4  +  6  =  10  9  +  6  =  15 

5  +  5  =  10  10  +  5  =  15 

5  +  6  =  11  10  +  6  =  16 

y>^c 


liESSOX   XIII. 

1.  How  many  apples  are  1  apple,  2  apples  and  3 
apples?     2  apples,  4  apples  and  1  apple? 

2.  If  you  put  2  dol- 
lars, 3  dollars  and  4  dol- 
lars into  an  empty  purse, 
how  many  dollars  will 
there  be  in  the  purse? 
2+3+4=? 

3.  How  many  are  9  and  6  ? 

4.  How  many  are  8  and  5? 

5.  Walter  caught  2  fishes,  Harry  caught  5,  and 
Webster  caught  3.  How  many  fishes  did  they  all 
catch? 


6  and  9? 
5  and  8? 


22  FIRST    LESSONS 

6.  Arthur  had  7   chickens,    and   his   father   gave 
him  6  more.      How  many  had  he  then? 

7.  3  +  3  +  7=-?     4  +  1  +  6  =  ?     3  +  2  +  8  =  ? 

8.  How  many  are  3  books,  5  books  and  6  books? 

9.  How  many  are  3  slates,  4  slates  and  5  slates? 

10.  There  are  5  birds  in  one  nest  and  4  in  another. 
How  many  birds  are  there  in  both  nests? 

11.  How  many  are  10  and  3?     3  +  10  =  ? 

12.  How  many  are  10  and  4?     4  and  10? 
13.2  +  3  +  5  =  ?     2  +  2  +  2  =  ?     1  +  5  +  6  =  ? 

14.  What  is  addition  ?  What  is  the  sign  of  ad- 
dition? 

15.  What  is  the  sign  of  addition  called? 

16.  Make  the  signs  used  in  addition. 

17.  In  one  nest  there  were  5  little  birds,  in  an-* 
other  4,  and  in  another  4.      How  many  birds  were 
there  in  these  nests? 

18.  In  a  school  5  pupils  were  tardy  on  Monday, 
2  on  Tuesday,  3  on  Wednesday,  3  on  Thursday,  and 
0  on  Friday.  How  many  pupils  were  tardy  during 
the  week? 

Slate  Exercises. 

Copy  and  add  the  following: 

2  3  4  4  6  7  1 

4  2  12  2  3  5 

8  5  6  5  3  3  6 

Copy  and  read  the  following: 

20       18       15       17      13       12       11       19 


IN    ARITHMETIC.  23 

LT]SSO]S^    XIV. 

1.  If  a  darning-needle   costs  1   cent,  and  a  skein 
of  silk  7  cents,  what  will  both  cost? 

2.  How  many  skeins  are  2  skeins  and  7  skeins? 

3.  If    there    are    3 

spools     in     one    group  — 

and  7  in  another,  how 
many  spools  are  there 
in  both  groups? 

4.  ^  A     woman     who 
had  4  quarts  of  cherries, 
bought   7    quarts.     How  many  did   she    then    have? 
4+7  =  ? 

5.  There  are  5  boys  in  one  group  and  7  in  an- 
other.    How  many  boys  are  there  in  both  groups? 

6.  There  are  6   cows  in  one  field  and  7   in  an- 
other.    How  many  cows  are  there  in  both  fields? 

7.  How  many  are   7   and  7?     How  many  are  8 
and  7? 

8.  How  many  are  9  and   7?     How  many  are   10 
and  7? 

9.  If  I  have  1  dollar,  and  my  brother  gives  me 
8  dollars,  how  many  dollars  will  I  then  have? 

10.  How  many  chairs  are  2  chairs  and  8  chairs? 

11.  How  many  are   3   and   8?     How  many  are   4 
and  8? 

12.  George  walked  a  distance  of  5  miles  one  day,, 
and  8   miles   the   next   day.     How  far   did  he  walk 
in  both  days?     5  +  8  =  ? 


24 


FIRST     LESSONS 


13.  6  +  8  =  ?     7  +  8  =  ?     8  +  8  =  ?     9  +  8=? 

14.  There  are  10  girls  in  one  class  and  8  in  an- 
other.    How  many  girls  are  there  in  both  classes? 

15.  Form  the  addition  tables  of  sevens  and  eights. 

TABLES. 


1  +  7=  8  6  +  7  =  13 

1  +  8=  9  6  +  8  =  14 

2  +  7=  9  7  +  7  =  14 

2  +  8  =  10  7  +  8  =  15 

3  +  7  =  10  8  +  7  =  15 

3  +  8  =  11  8  +  8  =  16 

4  +  7  =  11   9  +  7  =  16 

4  +  8  =  12  9  +  8  =  17 

5  +  7  =  12  10  +  7  =  17 

5  +  8  =  13  10  +  8  =  18 

:>U^c 


I^ESSO]^   XV. 

1.  How  many  peaches  are  7  peaches,  2  peaches 
and  5  peaches?     7  +  2  +  5=? 

2.  A  man  gave  4  dollars  for  corn  and  8  dollars 
for  a  ton  of  hay.     How  much  did  he  pay  for  both  ? 

3.  A  man  has  2  cows  in  one  pasture,  4  in  an- 
other, and  7  in  another.  How  many  cows  has  he 
in  the  three  pastures? 

4.  A  woman  sold  5  dozen  eggs  at  one  time,  4 
dozen  at  another  time,  and  8  dozen  at  another.  How 
many  dozen  did  she  sell? 

5.  A  woman  sold  7  pounds  of  butter  at  one 
time,  3  at  another  time,  and  5  at  another.  How 
many  pounds  did  she  sell? 


IN    ARITHMETIC.  25 

6.  6  +  3  +  2-=?     4  +  5  +  7  =  ?     3  +  2  +  5  =  ? 

7.  How  many  are  9  and  4?     4  and  9? 

8.  How  many  are  10  and  7?     7  and  10? 

9.  8  +  5  +  7  =  ?     3  +  7  +  5  =  ?     8  +  6  +  3  =  ? 

10.  A  farmer  paid  5  dollars  for  sugar,  2  dollars 
for  coffee,  and  10  dollars  for  flour.  What  was  the 
cost  of  the  whole? 

11.  How  many  are  8  boys,  2  boys  and  5  boys? 

12.  8  +  3  +  2  =  ?     3  +  2  +  6  =  ?     5  +  2  +  4  =  ? 

Slate  Exercises. 

Copy  and  add  the  following : 

673835648 
256145221 
223256343 


3>a^c 


i.esso:n^  XVI. 

1.  There  is  1  man  on  the  steps  and  there  are  9 
men  in  the  store.  How  many  men  are  there  in  both 
places  ? 

2.  Henry  sold  2  books  on  Tuesday  and  9  books 
on  Wednesday.  How  many  books  did  he  sell  in  both 
days? 

3.  How  many  shells  are  3  shells  and  9  shells? 

4.  How  many  boats  are  4  boats  and  9  boats? 

5.  If  Jennie  is  5  years  old,  and  her  sister  is  9 
years  older,  how  old  is  her  sister? 

3 


26 


FIRST    LESSONS 


6.  How  many  are  6  and  9?     7  and  9? 

7.  There  are    8  trees  in  one  row  and   9   in   an- 
other.    How  many  trees  are  there  in  both  rows? 

8.  How  many  plants  are  9  plants  and  9  plants? 

9.  How  many  books  are  10  books  and  9  books? 
10.  A  beggar  had  1  cent,  and  a  boy  gave  him  10 

cents.     How  many  cents  did  he  have  then? 

11.  If  there  are  2  straw- 
berries on  one  stem  and  10 
on  another,  how  many  are 
there  on  both  stems? 

12.  How  many  are  3  or- 
anges and  10  oranges? 

13.  4  +  10  =  ?  5  +  10  =  ? 
6  +  10  =  ? 

14.  A  boy  paid  7  shil- 
lings for  oil  and  10  shillings  for  a  lamp.  What 
was  the  cost  of  both  ?     7  +  10  =  ? 

15.  How  many  are  8  pigeons  and  10  pigeons? 

16.  How  many  are  9  and  10?     10  and  10? 

17.  Form  the  addition  tables  of  nines  and  tens. 


TABLES. 


1+9=10 

6+9=15 

1+10=11     6+10=16 

2+9=11 

7+9=16 

2+10=12     7+10=17 

3+9=12 

8+9=17 

3+10=13     8+10=18 

4+9=13 

9+9=18 

44-10=14     9+10=19 

5+9=14 

10+9=19 

5+10=15  10+10=20 

-^ 


IN    ARITHMETIc/'g^JY^v27 


liESSON   XVII, 


'k 


■rm.tl 


1.  Ruth  picked  4  pinks  from  one  stem,  3  from 
another,  and  2  from  another.  How  many  pinks  did 
she  pick? 

2.  If  there  are  6  boys  in  one 
class,  7  boys  in  another,  and  5  boys 
in  another,  how  many  boys  are 
there  in   the   three    classes  ?     6  +  7 

3.  2  +  2  +  2  =  ?  3  +  3  +  3  =  ? 
5+5+5=?     6+6+6=? 

4.  Begin  with  2  and  count  to  8 
by  2's ;  thus :  Two,  four,  six,  eight. 

5.  Begin  with  3  and  count  to  15  by  3's. 

6.  Begin  with  1  and  count  to  19  by  3's. 

7.  How  many  bells  are  5  bells,  2  bells,  6  bells 
and  4  bells?     5  +  2  +  6  +  4  =  ? 

8.10+5  +  3  +  4  =  ?     6  +  8  +  4  +  2  =  ? 
9.     2  +  3  +  6  +  1  =  ?     3  +  2  +  4  +  7  =  ? 

10.  Count  to  20  by  5's.     To  18  by  6's. 

11.  A  merchant  sold  5  yards  of  calico  to  one  girl, 
3  yards  to  another,  and  6  to  another.  How  many 
yards  did  he  sell? 

12.  Begin  with  2  and  count  to  17  by  3's. 

13.  How  many  are  7  barrels,  6  barrels  and  4 
barrels? 

14.  How  many  are  8  and  7  and  3? 

15.  Lucy  had  8  pins,  and  found  10  more.  How 
many  had  she  then? 


28  fikst   lessons 

Slate  Exekcises. 

Copy  and  add  the  following: 

941268513 
125510286 
432423625 
203331-544 


3»<00- 


LESSON  XTIII. 

1.  Jennie  gave  the  teacher  6  hyacinths,  Mary 
gave  her  4,  and  Minnie  gave  her  3.  How  many 
hyacinths  did  they  all  give  her?     6  +  4  +  3  =  ? 

2.  In  the  park  3  boys  are  flying  kites,  6  are  play- 
ing ball,  and  3  are  rolling  hoops.  How  many  boys 
are  there  in  the  park?     3  +  3  +  6  =  ? 

3.  There  are  4  soldiers  in  one  squad,  5  in  an- 
other, and  6  in  another.  How  many  soldiers  are 
there  in  the  three  squads? 

4.  How  many  are  4  guns,  5  guns  and  6  guns? 

5.  There  are  5  flags  on  one  building,  2  on  an- 
other, and  4  on  another.  How  many  flags  are  there 
on  the  three  buildings?     5  +  2  +  4  ==  ? 

6.  There  are  6  birds  in  one  cage,  2  in  another, 
and  7  in  another.  How  many  birds  are  there  in 
the  three  cages?     6  +  2  +  7  =  ? 

7.  1  +  2  +  6  +  9==?     8  +  1  +  5  +  3  =  ? 

8.  7  +  1  +  8  +  2  =  ?    3  +  3  +  3  +  3  =  ? 


IN    ARITHMETIC.  29 

9.  Jennie  is  8  years  old,    and   her   brother   is  5 
years  older.     What  is  the  age  of  her  brother? 

10.  Delia  has  1  doll,  Mina  has  2  dolls,  Carrie  has 
3  dolls,  and  Ruth  has  2  dolls.  How  many  dolls  have 
these  girls? 

11.  How  many  are  6  and  3  and  5?     6  +  3  +  5  =  ? 

12.  How  many  are  4  and  7  and  8?     4  +  7  +  8  =  ? 

13.  There  are  8  goblets  on  the  shelf,  6  on  the 
table,  and  4  on  the  stand.  How  many  goblets  are 
there  in  all? 

14.  A  wealthy  gentleman  had  3  draft-horses,  5 
riding-horses,  and  6  carriage-horses.  How  many 
horses  did  he  have? 

15.  A  gentleman  spent  4  months  of  every  year  in 
Florida,  2  months  in  the  White  Mountains,  3  months 
in  Europe,  and  the  rest  of  the  year  at  home.  How 
many  months  was  he  away  from  home? 

16.  James  wrote  6  lines  in  his  writing-book  on 
Monday,  3  lines  on  Tuesday,  7  lines  on  Wednesday, 
and  4  lines  on  Thursday.  How  many  lines  did  he 
write  in  those  four  days? 

17.  8  +  2  +  3  +  5  =  ?     7  +  3  +  4  +  4  =  ? 

Slate  Exercises. 

Copy  and  add  the  following: 

211648564 
253152344 
247321254 
264235424 


30  FIRSTLESSONS 

t 

REVIEW    EXERCISES. 

Find  the  value  of  each  of  the  following : 

5  +  4       6^8       6  +  3  9  +  4       8  +  1 

6  +  4       5  +  9      ^5  +  7  5  +  3       7  +  9 

7  +  6       2  +  8       8  +  3  6  +  4       8  +  8 

5  +  6       4  +  7       7  +  9  3  +  9       7  +  5 

3  +  9       3  +  5       9  +  3  4  +  4       6  +  3 

8  +  3  5  +  6  8  +  7  4  +  8  7  +  8 
Q  +  6  5  +  5  6  +  9  6  +  5  4  +  9 
8  +  4       4  +  9        5  +  8  7  +  6        5  +  7 

Add  the  following  without  using  slate : 

2  +  3  +  4  3  +  4  +  5  6  +  1  +  5 
7  +  2  +  5     6  +  5+3  2  +  9  +  2 

4  +  7  +  5     6  +  3  +  4  5  +  2  +  7 

6  +  5  +  8     4+9  +  6  5  +  6  +  8 

3  +  5  +  6     3  +  9  +  2  4  +  6  +  2 

3  +  5  +  6     7  +  5  +  4  7  +  3  +  5 

4  +  1  +  9  5  +  9  +  2  7  +  6  +  2 
6  +  8  +  3     5  +  3  +  4  4  +  7  +  5 

3  +  8  +  4     3+9  +  6  5  +  9  +  4 

2+5  +  4     2  +  7  +  3  6+1  +  5 

6  +  5  +  4  7  +  9  +  2  5  +  7  +  8 
3  +  1  +  6     5  +  2  +  7  6  +  3  +  4 

7  +  2  +  7  5  +  5  +  6  6  +  5  +  6 
3  +  7  +  2  3+2  +  5  5  +  7  +  6 
2  +  5  +  7  3  +  6  +  8  5  +  2+7 
7  +  3  +  5     4  +  6  +  5  6+5  +  4 


IN    ARITHMETIC.  -  31 

REVIEW    EXERCISES. 

Copy  and  add  the  following : 

875356  5  67 
4  6  9  8  4  4  12  2 
352682246 
42423783    5 


3 

6 

5 

5 

4 

6 

3 

2 

4 

4 

2 

3 

9 

7 

4 

2 

1 

2 

5 

3 

8 

4 

3 

1 

5 

6 

7 

4 

5 

1 

0 

1 

8 

4 

4 

6 

2 

2 

3 

2 

5 

1 

2 

5 

1 

Copy  and  add  the  following: 

3 -f  4+2  +  6  2  +  4+2  +  3  2  +  6  +  8  +  4 

3+2+1+6  4+8+2+4  2+6+1+7 

4+2+3+9  8+1+7+4  8+4+2+5 

4+7+4+3  6+4+2+7  5+2+7+6 

7+2+9+1  5+6+4+3  9+2+6+3 

4+2+6+5  4+9+2+4  5+2+7+6 

5+2+4+3  7+4+6+1  9+1+4+2 

8+2+6+3  9+1+4+5  4+2+6+7 

5+2+7+4  5+9+2+3  8+7+2+2 

4+3+5+8  4+7+6+2'  6+2+3+5 

5+4+9+2  9+2+3+6  4+7+2+6 

5+1+4+9  6+3+1+8  4+7+5+4 

7+3+3+7  6+4+4+6  8+2+2+7 

9+1+6+3  8+5+2+4  7+7+2+3 


32 


FIRST    LESSONS 


T.ESSON   XIX. 


1.  Make  two   marks  on  your  slates.     Erase  one. 
How  many  marks  are  there  left? 

2.  1  mark  from  2  marks  leaves  how  many  marks? 

3.  If  there    were    3    pencils    on    the    table,    and 
Helen  took  1  away,  how  many  were  left? 

4.  How  many  are  3  pencils  less  1  pencil  ? 

5.  If  4  apples  were  put  in  a  box,  and  afterward 
1  was  taken  out,  how  many  remained? 

6.  How  many  are  4  apples  less  1  apple? 

7.  Hold    up    5    fingers.     Put    one    down.     How 
many  fingers  are  you  holding  up? 

8.  How  many  are  5  fingers  less  1  finger? 

9.  Make  6  dots  on  your  slates.     Erase  one.     How 
many  are  there  left? 

10.  How  many  are  6  dots  less  1  dot? 

11.  How  many  steamships  are  represented  in  the 
picture  ? 

12.  If  1  sails  away,  how  many  are  left? 

13.  How  many  vessels  are  7  vessels  less  1  vessel? 

14.  How  many  boats  do  you  see  in  the  picture? 


IN    ARITHMETIC 


33 


15.  How  many  are  being  rowed  away  ?     How  many 
are  left? 

16.  How  many  boats  are  8  boats  less  1  boat? 

17.  If  there  are  9  trees,  and  a  man  cuts  1  down, 
how  many  will  be  left? 

18.  How  many  trees  are  9  trees  less  1  tree? 


3j*iC 


I^ESSON   XX. 

1.  A  rose-bush  had  3  roses  on  it,  but  1  dropped 
off.     How  many  roses  were  there  left  on  the  bush? 

2.  How  many  are  3  less  2? 

3.  Make  4  marks.  Erase  2. 
How  many  are  left? 

4.  How  many  marks  are  4 
marks  less  2  marks? 

5.  Helen  had  5  pennies,  and 
gave  2  to  a  beggar.  How  many 
had  she  left  ? 

6.  How  many  are  5  less  2? 

The  sign  —  takes  the  place  of  the  word  less.  It 
is  read  minus.  Thus,  4  less  2  equals  2,  is  written 
4  —  2  =  2,  and  is  read  4  minus  2  equals  2  ? 

7.  If  you  take  2  apples  from  a  group  of  6  apples, 
how  many  apples  will  be  left? 

8.  How  many  apples  are  6  apples  less  2  apples? 

9.  Express  6  less  2  equals  4.     6  —  2  =  4. 


34 


FIRST    LESSONS 


10.  William  had  7  pennies,  and  gave  2  for  a  pen- 
cil.    How  many  had  he  left?     7  —  2  =  ? 

11.  How  many  slates  are  8  slates  less  2  slates? 

12.  How  many  are  9  less  2?     How  many  are  10 
less  2?     How  many  are  11  less  2? 

13.  How  many  are  12  dollars  less  2  dollars? 

Taking  one  number  from  another  is  called  Sub- 
traction, 

14.  Form  the  subtraction  tables  of  ones  and  twos. 


TABLES. 


1  —  1=0 

6-1 

L  =  5 

2  —  2  =  0      7  —  2  =  5 

2  —  1  =  1 

7  —  ] 

L  =  6 

3  —  2  =  1      8  —  2  =  6 

3  —  1  =  2 

8-1 

L  =  7 

4  —  2  =  2      9  —  2  =  7 

4  —  1=3 

9-1 

[  =  8 

5  —  2  =  3    10  —  2  =  8 

5  —  1  =  4 

10—] 

L  =  9 

6  —  2  =  4    11  —  2  =  9 

3>»<C 


i:.esso:n^  xxi. 

1.  Helen  had  3  cents,  and  gave  them  for  a  pen- 
cil.    How  many  cents  had  she  left?     3  —  3  =  ? 

2.  A   man    had    4   horses,    and    sold   3   of  them. 
How  many  had  he  left?     4  —  3=? 

3.  How  many  cows  are  5  cows  less  3  cows? 

4.  A  boy  had  6  marbles,  and  gave  away  3.     How 
many  marbles  had  he  left?     6 — 3  =  ? 


IN    ARITHMETIC.  85 

5.  How  rnany  dollars  are  7  dollars  less  3  dollars? 
How  many  are  8  less  3? 

6.  A  woman  had  9  dollars,  and  gave  3  for  a  hat. 
How  many  dollars  had  she  left? 

7.  How  many  horses  are  10  horses  less  3  horses? 
How  many  are  11  minus  3? 

8.  If  there  were   12    pigeons   on   a  limb,   and  3 
flew  away,  how  many  remained?     12  —  3  =  ? 

9.  If  James  had  4  apples,  and  gave  away  4,  how 
many  had  he  left?     4  —  4  =  ? 

10.  If  Emily  had   5  cents,   and  gave  4  cents  for 
paper,  how  many  cents  had  she  left? 

11.  How  many  are  6  less  4?     7  minus  4  are  how 
many? 

12.  How  many  are  8  less  4?     9  minus  4  are  how 
many  ? 

13.  How  many  are  10  books  less  4  books?     11  hats 
less  4  hats? 

14.  How  many  are  12  minus  4?     13  less  4  are  how 
many  ? 

15.  Form  the  subtraction  tables  of  threes  and  fours. 

TABLES. 


3  —  3  =  0      8  —  3-5 

4  —  4  =  0      9  —  4  =  5 

4—3  =  1       9  —  3  =  6 

5  —  4=1     10  —  4  =  6 

5  —  3  =  2     10  —  3  =  7 

6  —  4  =  2     11—4  =  7 

6  —  3  =  3    11  —  3  =  8 

7  —  4  =  3    12  —  4  =  8 

7  —  3  =  4    12  —  3  =  9 

8—4  =  4    13  —  4  =  9 

36 


FIRST    LESSONS 


LESSON    XXII. 


1.  There  were  7  cents  in  a  box,  and  William 
took  out  3.     How  many  cents  were  left  in  the  box^^ 

2.  A  merchant  bought  12  lamps,  and  sold  4  of 
them.     How  many  had  he  left? 

3.  John  has  10  marbles,  and  Henry  has  3.  How 
many  more  has  John  than  Henry  ? 

4.  A  woman  who  had  9  yards  of  calico,  used  4 
yards.     How  many  yards  had  she  left? 

5.  8  —  2--?       9  —  2  =  ?     10  —  3  =  ? 

6.  6  —  3  =  ?     13  —  4  =  ?     11  —  4  =  ? 

7.  A  man  bought  9  barrels  of  flour,  and  sold  all 
but  3  of  them.  How  many  barrels  did  he  sell? 
9  —  3  =  ? 

8.  A  man  bought  a  boat  for  11  dollars,  and  sold 
it  for  4  dollars.     How  much  did  he  lose? 

9.  3  from  12  leave  how  many?     12  —  3  =  ? 

10.  William  had  10  cents.  He  spent  1  cent  for 
a  pencil  and  3  cents  for  paper.  How  many  cents 
had  he  left? 

11.  Carrie  had  12  apples,  but  she  gave  2  to  her 
sister  and  1  to  her  brother.  How  many  apples  had 
she  left? 

12.  How  many  are  6  less  2?  9  less  1  are  how 
many  ? 

13.  There  were  11  passengers  in  a  stage-coach,  5 
of  whom  got  out.     How  many  remained  ? 

14.  8  —  3  =  ?     7  —  1=?     12  —  4  =  ? 

15.  How  many  are  8  less  2?     8  —  2  =  ? 


in  arithmetic.  37 

Slate  Exercises. 

Copy,  subtract,  and  add  the  following : 

48         7         9         8         6         5         7 
24232132 


3^^C 


IjESSON   XXIII. 

1.  A  woman  had  5  quarts  of  berries,  and  sold  5 
quarts.     How  many  had  she  left?     5  —  5  =  ? 

2.  If  6  gallons  of  water  run  into  a  cistern  in  one 
hour,  and  5  run  out  in  the  same  time,  how  many  gal- 
lons remain  ?     6  —  5  =  ? 

3.  5  books  from  7  books  leave  how  many  books  ? 

4.  A  merchant  bought  8  penknives,  and  sold  5  of 
them.     How  many  had  he  left? 

5.  Henry  had  9  fish-hooks,  and  gave  5  of  them  to 
Martin.     How  many  had  he  left? 

6.  How  many  are  10  less  5?     11  less  5? 

7.  5  pencils  from  12  pencils  leave  how  many 
pencils  ? 

8.  5  from  13  leave  how  many?     5  from  14? 

9.  In  a  class  there  are  7  girls  and  6  boys.  How 
many  more  girls  are  there  than  boys? 

10.  From   a   bunch   of  8   keys,  6    keys  were   lost. 
How  many  keys  were  not  lost? 

11.  A  boy  having  9  pennies,  lost  6.     How  many 
had  he  left?     9  —  6  =  ? 


38 


FIEST    LESSONS 


12.  6  from  10  leave  how  many?     6  from  11  =  ? 

13.  How  many  are  12  less  6  ?     13  minus  6  are  how 
many  ? 

14.  A  farmer  who  had  14  bushels  of  potatoes,  sold 
6  bushels.     How  many  bushels  had  he  left? 

15.  How  many  are  15  boys  less  6  boys?     15  —  6 
=  2 

16.  Form  the  subtraction  tables  of  fives  and  sixes. 

TABLES. 


5  —  5  =  0    10  — 5-=5 

6  —  6  =  0    11  —  6  =  5 

6  —  5  =  1     11  —  5  =  6 

7  —  6  =  1     12  —  6  =  6 

7  —  5  =  2    12  —  5  =  7 

8  —  6  =  2    13  —  6  =  7 

8  —  5  =  3    13  —  5  =  8 

9  —  6  =  3    14—6  =  8 

9  —  5  =  4    14  —  5  =  9 

10  —  6  =  4    15  —  6  =  9 

Dj^C 


liESSON^   XXIV. 

1.  A  man  who  earned  7  dollars  a  week,  saved  only 
2  dollars.     How  much  did  he  spend?     7  —  2  =  ? 

2.  A  woman  bought  9  yards  of  calico,  and  used  5 
yards  of  it.     How  many  yards  had  she  left? 

3.  Henry  had  11  rabbits,  and  James  had  8.  How 
many  had  Henry  more  than  James? 

4.  Rush  is  14  miles  from  Geneseo,  and  Avon  is  9 
mile^  from  Geneseo,  on  the  same  road.  How  much 
farther  from  Geneseo  is  Rush  than  Avon? 


IN    ARITHMETIC. 


39 


,  6.  James  had  8  marbles,  but  lost  2  of  them. 
How  many  marbles  had  he  left?     8  —  2  =  ? 

6.  A  boy  caught  9  pig- 
eons, and  gave  4  of  them  to 
a  poor  woman.  How  many 
had  he  left?    ^  — 4  =  ? 

7.  If  6  gallons  of  water 
run  into  a  cistern  in  one 
minute,  and  5  gallons  run 
out,  how  much  is  the  cis- 
tern filled? 

8.  Ned  had  6  chickens, 
but  the  cat  killed  3  of  them.     How  many  were  left? 

9.  7  —  1=?       9  —  6  =  ?       8  —  5  =  ? 

10.  13  —  5  =  ?     15  —  4  =  ?     13  —  2  =  ? 

11.  How  many  sheep  are  9  sheep  less  3  sheep? 

12.  A  carriage-maker  had  15  carriages,  and  sold  9 
of  them.     How  many  had  he  left? 

- 13.  A  clothier  sold  8  coats,  6  of  which  were  for 
boys  and  the  rest  for  men.  How  many  of  the  coats 
were  for  men? 

14.  Martha  is  12  years  old,  and  Mary  is  4.     How 
many  years  older  than  Mary  is  Martha. 

15.  6  +  8  —  1=?    4  +  5  —  3  =  ?    3  +  7  —  2  =  ? 

16.  7  +  1  —  3  =  ?     5  +  3  —  6  =  ?     7  +  4  —  1  =  ? 

17.  How  many  are  7  and  3  less  2? 

-18.  In  a  basket  containing  12  oranges,  4  were  de- 
cayed.    How  many  were  sound? 
'19.  Amasa  picked  16  quarts  of  berries,  and  sold  6 
quarts  of  them.     How  many  quarts  had  he  unsold  ? 


40  fiest  lessons 

Slate  Exercises. 

Copy,  subtract,  and  add  the  following: 

97897847 
4         2         5         6         6         3         12 


aj^c 


LESSON    XXV. 

1.  Eichard  saw  8  ducks  in  a  pond,  7  of  which 
swam  away.     How  many  remained? 

2.  In  a  class  of  9  children  7  are  boys.  How 
many  are  girls  ?     9  —  7  =  ? 

3.  A  cooper  made  10  firkins,  and  sold  7  of  them. 
How  many  had  he  left?     10—7  =  ? 

4.  William  is  11  years  old,  and  Thomas  is  7. 
How  much  older  is  William  than  Thomas? 

5.  A  house  has  12  windows,  7  of  which  are  in 
the  first  story,  and  the  rest  in  the  second  story. 
How  many  are  there  in  the  second  story? 

6.  How  many  are  13  less  7?     14  less  7? 

7.  A  farmer  who  had  15  turkeys,  sold  7  of  them. 
How  many  had  he  left?     15  —  7==? 

8.  There  were  16  bottles  on  a  shelf,  7  of  which 
were  filled  with  pickles,  and  the  remainder  with 
fruit.     How  many  were  filled  with  fruit? 

9.  There  were  9  passenger-cars  on  a  railroad  track, 
8  of  which  were  filled  with  passengers.  How  many 
were  empty? 


IN    ARITHMETIC. 


41 


10.  How  many  are    10    less    8?     11    less   8?     12 
less  8? 

11.  A  merchant  had  13  barrels  of  salt,  and  sold 
8  of  them.     How  many  barrels  remained  unsold? 

12.  14—8-=?     15  —  8  =  ?     16  —  8  =  ? 

13.  How  many  are  17  trunks  less  8  trunks? 

14.  Form    the    subtraction    tables    of   sevens    and 

eights. 

TABLES. 


7  —  7=0  12  —  7  =  5 

8  —  8  =  0  13  —  8  =  5 

8  —  7=1  13  —  7  =  6 

9  —  8  =  1  14  —  8  =  6 

9  —  7=2  14—7  =  7 

10—8  =  2  15  —  8  =  7 

10—7=3  15  —  7  =  8 

11  —  8  =  3  16  —  8  =  8 

11  —  7=4  16  —  7  =  9 

12  —  8  =  4  17  —  8  =  9 

Dj^C 


IiESSO:N^    XXVI. 

1.  There  were  12  musk-rats  in  traps,  but  2  es- 
caped.    How  many  were  there  left  in  the  traps? 

2.  Helen  had  6  violets,  and  Jennie  had  16.  How 
many  more  had  Jennie  than  Helen? 

3.  What  number  added  to  6  makes  16  ? 

4.  5  +  8  +  2  —  5  =  ?     7  +  3  +  4  —  7  =  ? 

5.  Henry  gave  his  sister  12  figs.  She  gave  3  to 
Sarah  and  5  to  Flora.  How  many  had  she  left? 
12  — (3  +  5)=? 

6.  12  are  how  many  more  than  5? 
4 


42  FIRST    LESSONS 

7.  16  are  how  many  more  than  9? 

8.  What  number  added  to  8  makes  16? 

9.  What  number  added  to  5  makes  13? 

10.  Edgar  having  14  phims,  exchanged  5  of  them 
for  an  orange.     How  many  had  he  left? 

11.  How  many  are  14  less  8?     13  less  7? 

12.  Henry  caught  7  pigeons  at  one  time,  3  at 
another,  and  then  sold  4  of  them.  How  many  had 
he  left?     7  +  3  —  4=-:? 

13.  Frank  earned  13  dollars  and  George  earned  6. 
How  many  dollars  more  did  Frank  earn  than  George  ? 

14.  There  were  11  trunks  on  a  baggage-wagon,  7 
of  which  the  baggage-man  left  at  the  depot.  How 
many  were  left  in  the  wagon? 

15.  Out  of  15  vases  which  were  in  a  basket  6 
were  broken.     How  many  were  uninjured? 

16.  Mr.  Jones  planted  17  shade-trees,  but  5  of 
them  died.     How  many  lived? 

17.  In  a  class  of  19  all  but  6  were  promoted. 
How  many  were  promoted? 

18.  There  were  14  persons  on  board  a  ship  that 
was  wrecked,  of  whom  8  were  saved.  How  many 
were  lost? 

19.  16  +  ?=-18.       18  — ?=-12.      13  +  ?  =  19. 

Slate  Exercises. 
Copy,  subtract,  and  add  the  following: 
97867587 
33424231 


IN    ARITHMETIC. 


43 


LESSOIST   XXVII. 


1.  Eobert's  father  gave  him  10  doves,  but  9  of 
them  died  because  they  were  not  properly  cared  for. 
How  many  of  them  lived? 

2.  Eva  solved  11  exam- 
ples, 9  of  which  were  correct. 
How  many  were  wrong? 

3.  A  painter  bought  12 
gallons  of  oil,  and  used  9 
gallons.  How  many  gallons 
had  he  left? 

4.  A  grocer  bought  13  casks  of  vinegar,  and  sold 

9  casks.     How  many  casks  had  he  left? 

5.  How  many  are  14  less  9?  How  many  are  15 
less  9?     15  —  9=-?     15  — ?  =  9. 

6.  From  a  group  of  16  boys  9  ran  away.  How 
many  were  left?     16  —  9  =  ?     16  — ?  =  9. 

7.  9  from  17  leave  how  many?     17  —  9==? 

8.  How  many  are  18  less  9?      18  —  9  =  ? 

9.  A  merchant  bought  11  chests  of  tea,  and  sold 
all  but  1  of  them.      How  many  did  he  sell?     11  — 

10  =  ?     11_?:=10. 

10.  A  boy  had  12  steel-pens,  and  gave  away  10 
of  them.      How  many  had  he  left? 

11.  A  man  bought  13  tons  of  hay,  and,  after  feed- 
ing 10  tons  to  his  horses,  sold  the  rest.  How  many 
tons  did  he  sell?     13  —  10  =  ?     14  —  10  =  ? 

12.15  —  10  =  ?     16  —  10  =  ?     17  — lj[V=^f' 
13.  18  —  10  =  ?     18  — ?  =  10.    lO-l-Z^-lS. 


li- 


44 


FIRST    LESSONS 


14.  A  merchant  bought  18  whips,  and  sold  all  but 
How  many  did  he  sell?     18  —  8  =  ? 

15.  How  many  are  19  stoves  less  10  stoves? 

16.  Form  the  subtraction  tables  of  nines  and  tens. 


TABLES. 


9_9--0  14  —  9  =  5 

10—9  =  1  15  —  9  =  6 

11  —  9  =  2  16  —  9  =  7 

12  —  9  =  3  17  —  9  =  8 
13_9  =  4  18  —  9  =  9 


10  —  10  =  0  15—10  =  5 

11  —  10  =  1  16  —  10  =  6 

12  —  10  =  2  17  —  10  =  7 

13  —  10  =  3  18  —  10  =  8 

14  —  10  =  4  19  —  10  =  9 


5>»iC 


liESSO?^    XXTIII. 

1.  Begin  with  1  and  count  to  11  by  2's. 

2.  Begin  at  11  and  count  back  to  1  by  2's. 

3.  Count  15  by  3^s.     Count  16  by  4's. 

4.  Count  back  from  15  to  0  by  3's. 

5.  Count  back  from  20  to  0  by  5's. 

6.  Henry  had  fifteen  dollars.  He  gave  2  dollars 
for  a  hat,  3  dollars  for  a  vest,  and  6  dollars  for  a 
coat.     How  much  had  he  left? 

7.  What  number  added  to  3  makes  10? 

8.  What  number  added  to  9  makes  17? 

9.  A  harness-maker  having  19  harnesses,  sold  all 
but  9.     How  many  did  he  sell?     19  — ?  =  9. 


IN    ARITHMETIC.  45 

10.  How  many  are  2  +  2?  2  +  12?  3  +  2?  3 
+  12?     4  +  2?     4  +  12?     5  +  2?     5  +  12? 

11.  How  many  are  3  +  3?  3  +  13?  4  +  5?  4 
+  15?     5  +  6?     5  +  16?     7  +  6?     7  +  16? 

12.  How  many  are  3  +  6?  3  +  16?  4  +  6?  4 
+  16?     5  +  8?     5  +  18?     5  +  9?     5  +  19? 

13.  How  many  are  3  +  5?  3+15?  4  +  5?  4 
+  15?     8  +  6?     8  +  16?     8  +  7?     8  +  17? 

14.  In  the  barn  were  12  horses,  but  5  of  them 
were  taken  out.     How  many  remained? 

15.  10  chestnuts  from  16  chestnuts  leave  how  many 
chestnuts?     16  —  10  =  ? 

16.  A  grocer  bought  19  brooms.  He  sold  3  at  one 
time,  5  at  another,  and  4  at  another.  How  many 
had  he  left?     19  —  3  +  5  +  4=-? 

17.  A  lady  purchased  4  dollars'  worth  of  silk,  3 
dollars'  worth  of  velvet,  7  dollars'  worth  of  lace,  and 
1  dollar's  worth  of  linen.  She  gave  in  payment  20 
dollars.     How  much  should  be  returned  to  her? 

Slate  Exercises. 

Copy  and  add  the  following: 

4  5  3  2  6  1 

4  5  3  2  6  1 

4  5  3  2  6  1 

Copy  and  subtract  the  following: 

896789775 
652523413 


46 


FIRST    LESSONS 


LESSOINr    XXIX. 


A  man  having  18  butter-tubs,  sold  3  at  one 
5  at  another,   and  6  at  another.      How  many 
tubs  had  he  left? 

2.  In  a  room  there  are  14  flower- 
pots. There  are  4  in  one  window,  5  in 
another,   and   the   rest   are   in   the  third 

^r      window.      How   many  are   there   in   the 
<^li/,J^      third  window? 

3.  On  the  first  vine  there  are  12 
bunches  of  grapes,  on  another  there  are 
3  bunches,  and  on  another  4  bunches. 
How  many  bunches  more  are  there  on 
the  first  vine  than  on  the  other  two? 
12  — (3-1-4)=? 

4.  How   many   are   7   and   5   less   3? 

5.  There  are  13  boys  playing  ball, 
and  5  playing  marbles.  How  many 
more  are  there  playing  ball  than  there 
are  playing  marbles?      13  —  5  =  ? 

6.  What  is  meant  by  the  term  addi- 
)n?     What  is  meant  by  the  term  subtraction? 

7.  Julia  is  9  years  old,  and  her  sister  is  5  years 
der.     What  is  the  age  of  her  sister? 

8.  Charles  is  6  years  old,  and  James  is  17  years 
d.     How  much  older  than  Charles  is  James? 

9.  What  number  added  to  7  will  make  15? 
10.  What  number  added  to  5  will  make  12? 


IN    ARITHMETIC.  47 

11.  Begin  with  2  and  count  to  17  by  3's. 

12.  Count  from  19  back  to  1  by  3's. 

13.  What  number  subtracted  from  18  will  leave 
10?     18  — ?=10.      18  —  10  =  ? 

14.  What  number  subtracted  from  16  will  leave 
9?     16  — ?  =  9.     16  —  9=? 

15.  In  a  school  of  18  pupils  all  but  3  study  ge- 
ography.    How  many  study  geography? 

16.  James  attended  school  17  weeks,  but  Henry  at- 
tended only  8  weeks?  How  many  weeks  did  James 
attend  more  than  Henry?     17  —  8  =  ? 

17.  Julius  had  written  all  but  5  lines  on  a  page 
of  his  writing-book.  If  the  book  had  19  lines  on 
a  page,  how  many  had  he  written? 

18.  How  many  are  3  +  3  +  2  +  2  —  4+5  —  2  +  7? 

19.  How  many  are  5  +  7  +  1  —  3  —  2  +  5  —  9  +  8? 

20.  How  many  are  6  +  4  +  5  —  3  —  6  —  2  +  8  +  9? 

21.  How  many  are  8  —  3  +  2  —  3  +  6  +  2—6  +  2? 

22.  How  many  are  6  +  8  —  7  —  2  +  5  +  6  +  1—4? 

Slate  Exercises. 

Copy  and  add  the  following: 

56456532 
4  2  2  12  9  4  3 
35184657 

Copy  and  subtract  the  following: 

69864987 
55712342 


48  FIRST    LESSONS 

REVIEW   EXERCISES. 

Find  the  value  of  each  of  the  following : 


8-2 

9-3         8- 

-4 

9-6 

6-2 

7  —  5 

8  —  3         7- 

-5 

6-3 

8  —  7 

4  —  1 

9  —  4         7- 

-2 

9-2 

8-3 

6  —  6 

6  —  1         8- 

-2 

6-4 

7  —  3 

7  —  2 

5  —  2         6- 

-4 

8  —  3 

9-7 

8  —  5 

9  —  4         8- 

-1 

6  —  5 

7-3 

12-4 

15  —  6       13- 

-6 

14—9 

16-6 

15-6 

17  -  9       12  - 

-8 

11  —  4 

15-7 

13  —  4 

10-5       14- 

-9 

13-9 

11  —  8 

18  —  9     : 

17—8       10- 

-8 

11-8 

16-9 

15  —  6 

13  _  7       15- 

-6 

12-7 

14-5 

ind  the  vaL 

Lie  of  the  following,  without  using  slat 

3  +  2-4 

4  +  6  —  5 

6  +  3-2 

5  +  6-8 

4  —  3  +  6 

9  —  4  +  2 

6  +  5-8 

5  +  6-9 

5  +  8  —  7 

6  +  9  —  5 

9- 

-5  +  2 

6  +  7  —  6 

4+7  —  3 

5  +  6-9 

8  +  7  —  9 

6  —  3  +  4 

8  +  5-3 

9-6-2 

9- 

-8  +  6 

8-3-4 

9  —  6  +  5 

9  +  5-6 

8  +  2-6 

9-3+2 

7  —  2  +  5 

8  —  3  +  4 

6  +  3  —  8 

7  +  5  —  9 

8  —  4  +  3 

6  —  4  +  2 

7- 

-5  +  6 

9  —  7  +  2 

9  +  2-8 

8  +  6  —  9 

7  +  3-4 

9  —  4+2 

8  +  3  —  9 

8  —  6  +  2 

9- 

-7  +  3 

8-6-2 

8  —  2-4 

9-3  —  6 

8- 

-6  +  2 

8  +  6  —  9 

9  —  3  +  6 

9  +  2-8 

9- 

-6  +  4 

8-3  +  7 

6  —  4  +  2 

6-4-2 

8  +  3  —  9 

8  —  3  —  4 

IN    ARITHMETIC.  49 


REVIEW    EXERCISES. 

Copy  and  find  the  value  of  the  following: 

6  +  3  —  4  +  2—6  7  —  3  +  8  —  6  +  2 

5  —  3  +  7  —  2  —  6  8  —  3  +  6  —  5  —  4 

5  +  9  —  8  —  3  +  2  7  —  5  +  4  +  2  —  8 

9__3  +  2  — 6  +  4  9  —  3  —  4  +  6  +  2 

5  +  6  +  3  —  3  —  9  9  —  3  +  6-3-8 

8  +  3  —  7  —  4  +  2  5  +  2  —  3  +  6  —  4 

9  —  3  +  6  —  4  +  8  8  —  3  +  7  +  2  —  6 
9  —  4  +  3  +  2  —  6  9  —  4  +  3  +  2  —  8 
5+2  —  3  +  4  —  8  2  +  6  —  3  +  7  —  5 
9—3+4—3+2  6—3+4—6+2 
4+2  —  3  +  6  —  4  7  —  3  +  2  —  6  +  4 

When  an  example  has  several  numbers  inclosed  in  a  parenthesis, 
find  the  value  of  those  within  the  parenthesis  first,  and  then  of  this 
result,  and  the  rest  of  the  numbers. 

Thus,4  +  6  — (3  +  2  — 4)=4  +  6  — 1;  for  (3  +  2  — 4)  =  1. 

Copy  and  find  the  value  of  the  following: 

5  +  8— (3  +  6  — 2)  6  +  8  — (7  — 2  +  6) 

6 +  3 +  (4  — 3  +  2)  7  +  3  — (5  +  2  — 6) 

5  +  4  — (6  +  2  — 5)  9  — 2 +  (6  — 4  +  2) 

5  — 4  — (8  +  2  — 9)  8  +  6--(2  +  3  — 1) 

6  +  8  — (3  +  4  — 2)  8  — 4+ (8  —  6  +  4) 
9  — 3 +  (2 +  6  — 4)  9  +  8  — (8  — 3  +  2) 
9  +  6  — (3  — 2  +  7)  9  — 7— (8  — 6— 2) 
8  — 3 +  (2 +  6  —  3)  9  +  2  — (7  — 4  — 2) 
6  +  5— (6  — [8— 3])  2  +  6  — (3  — [4  — 3]) 


50  FIRST    LESSONS 


LESSON-   XXX. 

1.  How  many  quails  are  there  in  each  group? 

2.  Express  ten  on  your  slates. 

3.  How   many   quails    are   there   in    two   of  the 
groups  ? 

4.  How  many  are  1  ten  and  1  ten? 

5.  Express   2   tens,   or   twenty :    20.     What  does 
the  2  represent?     What  does  the  0  show? 

6.  Express  2  tens  and  1,  or  twenty-one :   21. 

7.  Express  2  tens  and  2  ones,  or  twenty-two. 

8.  Express  twenty-three,  twenty-four,  twenty-five, 
twenty-six,  twenty-seven,  twenty-eight,  twenty-nine. 

9.  Read  the  numbers  you  have  written. 

10.  How  many  quails  are  there  in  the  3  groups? 

11.  Express  3  tens,  or  thirty:  30.     What  does  the 
figure  3  represent?     What  does  the  0  show? 

12.  Express  3  tens  and  1,   or  thirty-one.      3  tens 
and  2  ones,  or  thirty-two. 

13.  Express   all   the   numbers   from   thirty-two  to 
thirty-nine. 

14.  Express  4  tens,  or  forty.     Express  4  tens  and 
1,  or  forty-one. 


IN    ARITHMETIC.  51 

15.  Express  the  numbers  from  forty-one  to  forty- 
nine. 

16.  When   two    figures   are    written    side    by  side, 
what  does  the  figure  at  the  right  represent? 

17.  What  does  the  figure  at  the  left  represent? 

18.  Write  all  the  numbers  from  one  to  forty-nine. 

19.  Express  in  words:   24,  32,  38,  47,  18,  29,  10, 
31,  49,  30. 

liESSON   XXXI. 

1.  Express  5  tens,  or  fifty:   50. 

2.  How  many  figures   are   required  to   represent 
the  number  fifty? 

3.  What  is  the  figure  at  the  right? 

4.  What  is  the  figure  at  the  left? 

5.  How  many  tens  are  there  in  fifty? 

6.  Express  5  tens  and  1,  or  fifty-one. 

7.  Write  the  numbers  from  fifty-one  to  fifty-nine. 

8.  Express  6  tens,  or  sixty :   60. 

9.  Write  the  numbers  from  sixty  to  sixty-ninco 

10.  Express  the  number  seventy. 

11.  How  many  tens  are  there  in  seventy? 

12.  How  many  ones  are  there  in  seventy?     How 
is  this  shown? 

13.  Write  the  numbers  from   seventy  to  seventy- 
nine.  Read  them. 

14.  Write   the    numbers    from    eighty   to    eighty- 
nine.  Read  them. 


52  FIRST    LESSONS 

15.  How  many  tens  and  ones  are  there  in  eighty- 
seven?     In  eighty-five?     In  eighty-eight? 

16.  Express  in  figures  the  numbers  from  eighty 
to  eighty-eight. 

17.  Write  8  tens  and  9  ones,  or  eighty-nine. 

18.  Express  9  tens,  or  ninety :   90. 

19.  Write  the  numbers  from  ninety  to  ninety-nine. 

20.  Ninety-nine  and  one  more,  make  how  many? 
One  hundred. 

21.  How  many  tens  are  9  tens  and  1  ten? 

22.  How  many  tens  are  there  in  one  hundred? 

23.  One  hundred  is  expressed  thus :    100, 

The  figure  0  at  the  right  shows  that  there  are  no 
ones,  the  0  next  to  it  shows  that  there  are  no  tens, 
and  the  figure  1  shows  that  there  is  one  hundred. 

When  three  figures  are  written  side  by  side,  the  fig- 
ure in  the  first  place  at  the  right  represents  ones,  the 
one  next  to  it  tens,  and  the  one  at  the  left  hundreds. 

Slate  Exercises. 

Express  in  figures  the  following : 

Thirty-two  Eighty  Forty-nine 

Ninety-six  Eighteen  Sixty-seven 

Eighty-four  Seventy-one  Thirty-three 

Forty-seven  Twenty-nine  Thirty-eight 

Copy  and  express  in  words  the  following: 
36  52  28  77  78 

84  81  39  29  55 


IN    ARITHMETIC.  53 


liESSOlS^   XXXII. 


*  1.  If  you  pay  1  cent  for  a  pear,  how  many  cents 
will  you  pay  for  2  pears? 

2.  How  many  cents  are  1  cent  and  1  cent? 

3.  If  you  pay  1  cent  for  a  slate-pencil,  how  many 
cents  will  you  pay  for  3  pencils? 

4.  How  does  the  price  of  3  pencils  compare  with 
the  price  of  1  pencil? 

5.  If  a  fig  costs  one  cent,  how  many  times  1  cent 
will  4  figs  cost? 

6.  How  many  chairs  are  5  times  1  chair? 

This  sign  X  takes  the  place  of  the  word  times. 
Thus,  2  times  1  are  2,  is  written  2X1  =  2,  and  is 
read  2  times  1   equals  2. 

7.  If  1  marble  costs  1  cent,  what  will  6  marbles 
cost?     6X1=^6. 

8.  Seven  boys  each  own  a  sled.  How  many  sleds 
do  they  all  own  ?     7  X  1  =  ? 

9.  Each  of  8  boys  has  a  pair  of  skates.  How 
many  pairs  do  they  all  own  ?     8  X  1  =  ? 

10.  Nine   men   each   own   an   acre  of  land.     How 
many  acres  do  they  all  own  ?     9  X  1  =  ? 

11.  How  many  are  10  times  1?     10  X  1=? 

12.  How  many  are  3  times  1  ?     3  X  1  =? 

13.  If  you  pay  1   cent   for   an    apple,   how  many 
cents  will  you  pay  for  7  apples? 

14.  If  each  pupil,  in  a  class  of  9  pupils,  answers 
1  question,  how  many  questions  will  they  all  answer? 


54  FIRST    LESSONS 


liESSON^   XXXIII. 

1.  A  horse  has  2  eyes.     How  many  eyes  have  2 
horses?     How  many  eyes  are  2  times.  2  eyes? 

2.  A  horse  has  2  ears. 
How  many  ears  have  3 
horses?     3X2==? 

~  3.  If  1  rocking-horse 
costs  2  dollars,  what  will 
4  rocking-horses  cost?  4 
X2  =  ? 

4.  If  a  boy  goes  to 
school  only  2.  days  each  week,  how  many  days  will 
he  attend  in  5  weeks? 

5.  A  boy  read  2  pages  of  his  book  each  day  for 
6  days.     How  many  pages  did  he  read  in  that  time? 

6.  If  a  boy  earn    2  dollars   a   week,  how   many 
dollars  will  he  earn  in  7  weeks  ?     7X2  =  ? 

7.  What  will  8  sheets  of  blotting-paper   cost  at 
2  cents  a  sheet?     8X2=? 

8.  What  will  9   pairs  of  shoes  cost  at  2  dollars 
a  pair?     9X2  =  ? 

9.  How    many    cents    are    there    in    10   two-cent 
pieces  ? 

10.  If  it  requires  2  yards  of  cloth  to  make  a  child's 
cloak,  how  many  yards  will  it  require  to  make  ^ 
such  cloaks? 

A  short  process  of  adding  equal  numbers  is  called 
Multiplication, 


IN    ARITHMETIC 


55 


11.  Form   the    multiplication   tables   of  ones   and 
twos. 

TABLES. 


1X1-1     6X1-   6 

1X2—   2     6X2  —  12 

2X1  —  2     7X1—   7 

2X2—   4     7X2  —  14 

3X1—3     8X1—   8 

3X2—   6     8X2  —  16 

4X1=4     9X1—   9 

4X2—   8     9X2  —  18 

5X1  —  5  10X1  —  10 

5X2  —  10  10X2  —  20 

3>>iC 


IjESSOX    XXXIV. 

1.  If  a  boy  walks  3  miles  in  1  hour,  how  many 
miles  will  he  walk  in  2  hours  ?     2X3  —  ? 

2.  What  will  3  engravings  cost  at  3  dollars  each  ? 
-  3.  Martha  put  3  tulip  bulbs  in  each  of  4  pots. 

How  many  bulbs  did  she  plant  ?     4X3  —  ? 

4.  Each  of  5  boys  threw  3  stones  into  the  water. 
How  many  stones  did  they  all  throw  ?     5X3  —  ? 

5.  If  the  pupils  learn  3  songs  in  a  month,  how 
many  songs  will  they  learn  in  6  months? 

6.  If  there  are  3  cherries  in  1  bunch,  how  many 
cherries  are  there  in  7  such  bunches? 

7.  If  there  are  8  boats,  and  3  boys  in  each  boat, 
how  many  boys  are  there  in  the  boats? 

8.  If  there   are    3    globes   on   1   chandelier,  how 
many  globes  are  there  on  9  such  chandeliers? 


56 


FIRST    LESSONS 


9.  If  a  boy  gives  4  cents  for  1  orange,  how  many 
cents  will  he  give  for  2  oranges  ?     2X4  =  ? 

10.  A  lumberman  put  4 
logs  in  the  river  each  day 
for  3  days.  How  many 
logs  did  he  put  in  the 
river?  How  many  are  3 
times  4?     3X4  =  ? 

11.  If  there  are  4  crows 
sitting  on  each  of  4  limbs 
of  a  tree,  how  many  crows 

are  there  on  the  tree  ?  4X4  =  ?  How  many  are  4 
times  4? 

12.  What  will  6  tons  of  hay  cost  at  4  dollars  a 
ton  ?     5X4  =  ? 

13.6X4  =  ?     7X4  =  ?     8X4  =  ?     9X4  =  ? 

14.  How  many  girls  are  there  in  10  groups  of  4 
girls  each  ?     10X4  =  ? 

15.  If  a  man  can  walk  4  miles  in  an  hour,  how 
far  can  he  walk  in  6  hours?     6X4  =  ? 

16.  Form  the  multiplication  tables  of  threes  and 
fours. 

TABLES. 


1X3=   3 

6X3  =  18 

1X4=   4 

6X4  =  24 

2X3=   6 

7X3  =  21 

2X4=   8 

7X4  =  28 

3X3=   9 

8X3  =  24 

3X4  =  12 

8X4  =  32 

4X3  =  12 

9X3  =  27 

4X4  =  16 

9X4  =  36 

5X3  =  15 

10X3  =  30 

5X4  =  20 

10X4  =  43 

IN    ARITHMETIC.  57 

liESSOlSr    XXXY. 

1.  If  1  man  builds  2  rods  of  fence  in  one  day, 
how  many  rods  can  5  men  build  in  the  same  time? 

2.  If  a  shoe-maker  makes  4  pairs  of  shoes  in  1 
day,  how  many  pairs  will  he  make  in  6  days? 
6X4-=? 

3.  If  a  turner  can  turn  3  rolling-pins  in  1  min- 
ute, how  many  can  he  turn  in  8  minutes?     8X3  =  ? 

4.  If  a  woman  sells  4  quarts  of  milk  a  day,  how 
many  quarts  does  she  sell  in  9  days  ?      9X4  =  ? 

5.  In  1  pint  there  are  4  gills.  How  many  gills 
are  there  in  5  pints  ?     5X4  =  ? 

6.  A  boy  bought  4  pints  of  chestnuts  at  3  cents 
a  pint,  and  sold  them  for  20  cents.  How  much  did 
he  gain  ?     4X3  =  ? 

7.  (5X3)-f(3X4)  =  ?      (4X2)  +  (6X3)=? 

8.  If  a  boy  husks  3  bushels  of  corn  in  1  hour,  how 
many  bushels  will  he  husk  in  7  hours  ?     7X3  =  ? 

9.  If  2  yards  of  lace  will  make  1  curtain,  how 
many  yards  are  required  to  make  4  curtains? 

10.  In   1   bushel  there   are  4   pecks.      How  many 
pecks  are  there  in  7  bushels  ?     7X4  =  ? 

11.  How  many  are  9  times  2?     7X2?     5X2? 

12.  If  there  are  4  blades  in  1   pocket-knife,  how 
many  blades  are  there  in  10  such  knives?     10  X  4  =  ? 

13.  What  will   be  the  cost  of  9  historical  charts 
at  3  dollars  each?     9X3  =  ? 

14.  If  in    1    field   there    are   4   acres,   how   many 
acres  are  there  in  4  such  fields  ?     4X4  =  ? 


58 


FIRST    LESSONS 


Slate  Exercises. 

Copy  and  multiply  the  following : 

3         2         4         3         2         4 
5         4         8         7         9         6 


>>©4c 


IiESSO:N^    XXXTI. 

1.  John  gave  5  cents  apiece  to  each  of  2  beggars. 
How  much  did  he  give  to  both  ?     2X5  =  ? 

2.  If  a  boat  sails  5 
miles  in  1  hour,  how 
far  will  she  sail  in  3 
hours?     3X5  =  ? 

3.  In  each  of  4 
nests  there  are  5  eggs. 
How  many  eggs  are 
there   in  the  4  nests? 

How  many  are  4  times  5  ?     4X5  =  ? 

4.  What  will  5  barrels  of  flour  cost  at  5  dollars 
a  barrel  ?     5X5  =  ? 

5.  A  cartman  can  draw  5  barrels  of  salt  at  1  load, 
How  many  barrels  can  he  draw  in  6  loads?  How 
many  are  6  times  5? 

6.  What  will  7  bunches  of  matches  cost  at  5  cents 
a  bunch  ?     7X5  =  ? 

7.  How  many  are  8  times  5?  How  many  are  9 
times  5  ? 


IN     ARITHMETIC.  59 

8.  How    many    cents    are    there    in    10   five-cent 
pieces?     10X5  =  ? 

9.4X5  =  ?     3X5  =  ?     7X5  =  ?     8X5  =  ? 

10.  There  are  6  lamps  on  each  of  2  shelves.  How 
many  lamps  are  there  on  both  shelves  ?     2X6=? 

11.  If  6  bushels  of  wheat  can  be  ground  in  1  hour, 
how  many  bushels  can  be  ground  in  3  hours?  How 
many  are  3  times  6? 

12.  If  a  boy  writes    6    lines   in    his  writing-book 
ach  day  for  4  days,  how  many  lines  will  he  write? 

How  many  are  4  times  6? 

13.  If  a  man  pays  6  dollars  at  5  different  times, 
how  many  dollars  will  he  pay?     5X6  =  ? 

14.  How  many  are  6  times  6?  How  many  are  7 
times  6? 

15.  In  1  package  there  are  6  drawing-pencils. 
How  many  pencils  are  there  in  8  such  packages? 
8X6  =  ? 

16.  How  many  are  9  times  6?  10  times  6  are 
how  many  ? 

17.  Form  the  multiplication  tables  of  fives  and 
sixes. 

TABLES. 


1X5=   5     6X5  =  30 

1X6=   6     6X6  =  36 

2X5  =  10     7X5  =  35 

2X6  =  12     7X6  =  42 

3X5  =  15     8X5  =  40 

3X6  =  18     8X6  =  48 

4X5  =  20     9X5  =  45 

4X6  =  24     9X6  =  54 

5X5  =  25  10X5  =  50 

5X6  =  30  10X6  =  60 

60  FIRST    LESSONS 


I.ESSON    XXXTII. 

1.  If  a  croquet-player  drives  a  ball  through  2 
arches  at  each  stroke,  through  how  many  arches 
will  he  drive  it  by  3  strokes  ?     3X2  =  ? 

2.  How  many  are  9  sleds,  2  sleds,  and  8  sleds? 

3.  A  boy  who  shot  18  prairie-chickens,  gave  2  to 
George,  3  to  Henry,  and  7  to  Caspar.  How  many 
had  he  left?     18  — (2  +  3  +  7)  =  ? 

4.  A  man  bought  6  bushels  of  wheat  at  2  dol- 
lars a  bushel,  and  8  bushels  of  barley  at  1  dollar  a 
bushel.     What  did  he  pay  for  both? 

5.  How  many  soldiers  are  there  in  4  squads  of 
5  soldiers  each? 

6.  (6X2)  +  (8X1)=?     (3X5)  +  (4X1)=? 

7.  (4X2)  +  (3X3)  =  ?     (2X5)  +  (2X3)=? 

8.  How  many  feet  have  4  dogs?      7  dogs? 

9.  How  many  eyes  have  6  horses?     9  horses? 

10.  How  many  legs  have  6  rabbits?     8  rabbits? 

11.  How  many  wings  have  10  birds?     7  birds? 

12.  From  a  bin  containing  16  bushels  of  potatoes 
4  bushels  were  taken  at  one  time,  and  6  at  another. 
How  many  bushels  remained  in  the  bin? 

13.  A  woman  had  a  jar  of  butter,  containing  20 
pounds.  She  used  5  pounds  one  week,  6  pounds 
the  next  week,  and  the  remainder  the  third  week. 
How  much  did  she  use  the  third  week? 

14.  There  are  3  feet  in  1  yard.  How  many  feet 
are  there  in  7  yards? 

15.  10  +  6  — (4X2)=?     12  — 3  +  (5X6)  =  ? 


IN    ARITHMETIC.  61 

16.  A  drover  had  6  cows  in  one  field,  8  cows  in 
another,  and  12  in  another.  How  many  cows  had 
he  in  the  three  fields? 

17.  If  a  girl  can  pick  3  quarts  of  berries  in  1 
hour,  how  many  quarts  can  she  pick  in  3  hours? 

Slate  Exercises 
Copy  and  multiply  the  following : 

6543273643 

5798947987 


>»-o<v- 


r.ESSOK    XXXTIII. 

1.  In  1  week  there  are  7  days.     How  many  days 
are  there  in  2  weeks?     2X7==? 

2.  How  many  rods  of  ditch  were  dug,  if  7  rods 
were  dug  each  day  for  3  days  ?     3X7  =  ? 

3.  If  there  are  7  pickets   in   1   gate,  how  many 
pickets  are  there  in  4  such  gates  ?     4X7  =  ? 

4.  How  many  tomatoes  are  there,  if  there  are  7 
tomatoes  on  each  of  5  plants  ?     5X7  =  ? 

5.  If  there    are   7   flags  displayed    at  each    of  6 
windows,  how  many  flags  are  displayed  ?     6X7  =  ? 

6.  What  will  a  man   receive  for  setting  7  panes 
of  glass  at  7  cents  a  pane  ?     7X7  =  ? 

7.  If  you  can   make  7  marks   in   1  second,  how 
many  marks  can  you  make  in  8  seconds  ?     8  X  7  =:  ? 


62  FIEST    LESSONS 

8.  If  it  takes  9  men  7  days  to  do  a  piece  of  work, 
how  long  will  it  take  1  man  to  do  it  ?     9X7  —  ? 

9.  How  much  will  Henry  earn   in  10  weeks,  if 
he  earns  7  dollars  a  week?     10X7=? 

10.  If  a  woman   packs   8   pounds  of  butter  in   1 
week,  how  much  will  she  pack  in  2  weeks  ?     2X8==? 

11.  What  will  3  pounds  of  raisins  cost  at  8  cents 
a  pound  ?     3X8  =  ? 

12.  How  many  are  4   times   8?      How  many  are 
5  times  8? 

13.  If  a   man  draws   8    loads  of  grain   in    1   day, 
how  many  loads  will  he  draw  in  6  days  ?     6X8  =  ? 

14.  If  there  are  8  candles  in  1  pound,  how  many 
candles  are  there  in  7  pounds  ?      7X8  =  ? 

15.  What  will  8  quarts  of  cherries  cost  at  8  cents 
a  quart?     8X8  =  ? 

16.  If  a  cooper  sells  8  barrels  each  day  for  9  days, 
how  many  barrels  will  he  sell  ?     9X8  =  ? 

17.  If  8  pupils  can  sit  on  1  seat,  how  many  pupils 
can  sit  on  10  such  seats?     10X8  =  ? 

18.  Form  the  multiplication  tables  of  sevens  and 
eights. 

TABLES. 


1X7=  7      6X7=42 

1X8=  8      6X8=48 

2X7=14      7X7=49 

2X8=16      7X8=56 

3X7=21      8X7=56 

3X8=24      8X8=64 

4X7=28      9X7=63 

4X8=32      9X8=72 

5X7=35    10X7=70 

5X8=40    10X8=80 

INARITHMETIC.  63 

liESSOlS^    XXXIX. 

1.  A  boy  having  24  cents,  bought  2  oranges  at  6 
cents  apiece.  How  many  cents  had  he  left?  24  — 
(2X6)=? 

2.  John  sold  3  bananas  at  8  cents  apiece,  and  2 
cups  of  peanuts  at  5  cents  a  cup.  What  did  he  re- 
ceive for  the  whole?  ' 

3.  Henry  solved  7  examples  on  Monday,  5  on 
Tuesday,  and  9  on  Wednesday.  How  many  exam- 
ples did  he  solve  in  the  three  days? 

4.  If  he  solved  16  examples  the  next  week,  how 
many  examples  more  did  he  solve  the  first  week  than 
the  second? 

5.  Count  to  50  by  lO's.     Count  to  30  by  5's. 

6.  How  many  are  2  and  4?  2  and  14?  2  and 
24?     2  and  34? 

7.  How  many  are  4  and  5?  4  and  15?  4  and 
25?     4  and  35? 

8.  How  many  are  5  and  6?  15  and  6?  25  and 
6  ?     35  and  6  ? 

9.  If  a  horse  eats  3  bushels  of  oats  in  one  week, 
how  many  bushels  will  he  eat  in  8  weeks? 

10.  AVhat  is  the  cost  of  7  cakes  of  soap  at  10  cents 
a  cake? 

11.  A  boy  Avorked  7  weeks  for  8  dollars  a  week, 
and  spent  20  dollars  for  clothes.  How  much  money 
had  he  left?     (7X8)  — 20  =  ? 

12.  If  a  wheel  has  only  7  spokes,  how  many  spokes 
will  7  such  wheels  have? 


64  FIRST    LESSONS 

13.  A  man  earns  16  dollars  a  week,  and  his  son 
earns  10  dollars.     How  much  do  they  both  earn? 

14.  How  much  more  does  the  father  earn  than 
the  son? 

15.  If  a  mechanic  earns  5  dollars  a  day  for  2  days, 
and  6  dollars  a  day  for  3  days,  how  much  money 
will  he  earn  in  that  time?     (2  X  5)  +  (3  X  6)  =  ? 

16.  A  boy  sold  2  chickens  for  3  dimes  each,  and 

2  dozens  of  eggs  at  2  dimes  a  dozen.     How  many 
dimes  did  he  receive? 

17.  What  will  be  the  cost  of  2  pairs  of  pantaloons 
at  6  dollars  a  pair,  and  3  vests  at  3  dollars  each? 

18.  What  will  be  the  cost  of  8  ounces  of  candy  at 
5  cents  an  ounce,  and  2  packages  of  envelopes  at  15 
cents  a  package? 

19.  How  many  days  are  there  in  7  weeks?  How 
many  are  7  times  7? 

20.  If  a  family  burns  8  tons  of  coal  worth  6  dol- 
lars a  ton,  and  5  cords  of  wood  worth  5  dollars  a 
cord,  how  much  will  the  fuel  cost? 

21.  If  4  chairs  are  bought  at  5  dollars  apiece,  and 

3  tables  at  6  dollars  each,  how  much  will  they  all 
cost? 

•     22.  4+5  +  (3X8)=?     (2X6)  +  5  — 3-? 

Slate  Exercises. 
Copy  and  multiply  the  following: 

876945768   5 
568476863   5 


I 


IN    AKITHMETIC. 


65 


1.  A  man  bought  2  loaves  of  bread  at  9  cents  a 
loaf.     How  much  did  they  cost  him  ?     2  times  9  =  ? 

2.  If  there  are  9 
rose-buds  in  one  bou- 
quet, how  many  rose- 
buds are  there  in  o 
such  bouquets? 

3.  If  it  require   9     !^' 
tons  of  coal  to  run  a 
train  of  cars  one  trip, 
how  many  tons  will  it 
require  to  run  4  such  trips  ?     How  many  are  4X9? 

4.  In   one   square   yard   there    are   9   square   feet. 
How  many  square  feet  are  there  in  5  square  yards? 

5.  At  9  dollars  a  barrel,  what  will  6  barrels  of 
flour  cost? 

6.  In  an  orchard  there  are  9  trees  in  a  row,  and 
7  rows.     How  many  trees  are  there  in  the  orchard? 

7.  What  will  8  pounds  of  nails  cost  at  9  cents  a 
pound? 

8.  When  sugar  is  selling  at  9  cents  a  pound,  how 
much  will  9  pounds  cost?      9X9  =  ? 

9.  How  many  cents  must  be  paid  for  10  yards  of 
muslin  at  9  cents  a  yard?     10  X  9  =  ? 

10.  Mary  is  10  years  old,  and  her  sister  is  twice 
as  old.     How  old  is  her  sister?     2  X  10  =  ? 

11.  There   are   10  cents   in   a  dime.      How   many 
cents  are  there  in  3  dimes?      3X10^=? 

6 


eQ 


Fill  ST    LESSONS 


12.  If  one   shelf  will   hold   10  books,   how   many 
books  will  4  such  shelves  hold  ?     4  X  10  =  ? 

13.  In  one  dollar  there  are  10  dimes.     How  many 
dimes  are  there  in  5  dollars  ?     5X10  =  ? 

14.  Henry   received   10  credit  marks   per   day   for 
6  days.      How  many  did  he  receive?     6X10  =  ? 

15.  If  10  marbles  can  be  bought  for  1  cent,  how 
many  can  be  bought  for  7  cents?     7  X  10  =  ? 

16.  If  there  are  10  weeks  in  one  term  of  school, 
how  many  weeks  are  there  in  8  terms?     8X10  =  ? 

17.  A   farmer   sold   9    hogs    at    10  dollars   apiece. 
How  many  dollars  did  he  get  for  them?     9  X  10  =  ? 

18.  If  sewing  needles  cost  10  cents  a  paper,  what 
will  10  papers  cost?     10X10  =  ? 

19.  Form   the   multiplication   tables  of  nines  and 
tens. 

TABLES. 


1X9=  9      6X9=54 

1X10=10     6X10=  60 

2X9=18      7X9=63 

2X10=20     7X10=  70 

3X9=27      8X9=72 

3X10=30     8X10=  80 

4X9=36      9X9=81 

4X10=40     9X10=  90 

5X9=45    10X9=90 

5X10=50  10X10=100 

Slate  Exercises. 

Copy  and  multiply  the  following : 

5        3        6        5        4        5        4 
4       2        3        7        3        8        7 


7 
10 


INAEITHMETIC.  67 


liESSON^    Xlil. 

1.  If  thera  are  8  goslings  in  the  water  and  6  on 
the    land,    how  many  goslings  are  there  altogether? 

2.  How    many    more    gos- 
lings  are   there    in   the  water 

than  there  are  on  the  land?  K"^-ri^r<,  ^z  :^ 

3.  Henry  has  7  sheep,  and        ^>^  ^{^ 
his  father  has  9  times  as  many.  -.    t2el„,,      ''4'^^ 
How  many  sheep  has  his  fa- 
ther? 

4.  How   many  sheep  have 

Henry  and  his  father?     How  many  are  63  and  7? 

5.  An  Indian  sold  8  baskets  at  10  cents  apiece. 
How  much  did  he  receive  for  them?     8X  10  =  ? 

6.  A  boy  having  6  rabbits,  bought  8  more,  and 
then  sold  9.      How  many  had  he  left? 

7.  Count  to  48  by  6's.      Count  to  63  by  7's. 

8.  Count  back  from  45  to  0  by  9's. 

9.  From  a  crock  of  butter  weighing  25  pounds 
7  pounds  were  taken  at  one  time,  3  at  another,  and 
6  at  another.     How  many  pounds  remained? 

10.  A  laundress  bought  at  one  time  3  flat-irons, 
each  weighing  6  pounds;  at  another  time  2  flat- 
irons,  each  weighing  8  pounds.  What  was  the  en- 
tire weight  of  the  irons? 

11.  At  8  dollars  a  term  each,  how  much  will  a 
music-teacher  receive  for  6  pupils  ?     6X  S  =  2 

12.  There  are  7  days  in  one  week.  How  many 
days  are  there  in  9  weeks?     7x9  =  ?     9X7  =  ? 


68  FIRST    LESSONS 

13.  If  a  horse  trot  9  miles  in  one  hour,  how  far 
will  he  travel  in  10  hours?     lOX  9  =  ?     9  X  10  =  ? 

14.  If  one  passenger-car  has  8  wheels,  how  many 
such  wheels  will  5  cars  have ?     5X8=^?     8X5  =  ? 

Slate  Exercises. 
Copy  and  multiply  the  following : 

789689787 
543595632 


3^^C 


IjE8So:n^  xlii. 

1.  A  cutler  sold  6  sets  of  knives  one  day,  5  sets 
the  next  day,  and  8  sets  the  next.  How  many  sets 
did  he  sell? 

2.  What  is  addition  ?  What  is  the  sign  of  addi- 
tion? 

3.  A  painter  having  13  pounds  of  paint,  used  6 
pounds  one  day  and  3  the  next.  How  many  pounds 
had  he  left?     13  — (6  +  3)=?     13  —  6  —  3  =  ? 

4.  What  is  subtraction  ?  What  is  the  sign  of  sub- 
traction ? 

5.  A  farmer  sold  3  sheep  at  4  dollars  apiece,  and 
6  calves  at  5  dollars  a  head.  What  did  he  receive 
for  the  whole?     (3  X  4)  +  (6  X  5)  =? 

6.  What  is  multiplication?  What  is  the  sign  of 
multiplication  ? 


IN    ARITHMETIC.  69 

7.8  +  5  +  6  =  ?     24  —  3  —  6  =  ?     8X2  =  ? 

8.  In  one  yard  there  are  3  feet.  How  many  feet 
are  there  in  4  yards?  How  many  feet  are  there  in 
5  yards? 

9.  If  a  squirrel  eats  8  nuts  in  one  day,  how  many 
nuts  will  he  eat  in  9  days?     9X8  =  ?     8X9  =  ? 

10.  What  will  be  the  cost  of  6  pears  at  6  cents 
each  ?     6X6  =  ? 

11.  In  one  peck  there  are  8  quarts.  How  many 
quarts  are  there  in  5  pecks  ?     5  X  8  ^^  ? 

12.  How  many  are  9  times  5?  How  many  are  7 
times  6? 

13.  There  are  4  classes  in  a  school,  each  class  con- 
taining 10  pupils.  How  many  pupils  are  there  in 
the  school?     4X  10  =  ? 

14.  In  an  orchard  there  are  7  rows  of  trees,  and 
9  trees  in  each  row.  How  many  trees  are  there  in 
the  orchard?      7X9  =  ?     9X7  =  ? 

15.  A  man  having  16  cords  of  wood,  used  all  but 
5  cords.     How  many  cords  did  he  use?     16  —  5  =  ? 

16.  Helen  gave  7  yards  of  cloth  to  a  poor  woman, 
and  had  9  yards  left.  How  many  yards  had  she  at 
first? 

17.  17  +  3  —  8  =  ?     21  —  6  =  ?     21  — (6  +  5)=? 

Slate  Exercises. 

Copy,  add,  subtract,  and  multiply  the  following : 

5         8         9         8       ^5         6         9     -     8 
37423244 


70  FIRST    LESSONS 

REVIEW   EXERCISES. 

Find  the  value  of  the  following : 

7X9     3X4  3X8  8X6    6X6 

6X5     8X5  5X4  7X3    3X9 

5X8     6X7  6XS  4X9    7X5 

4X7     3X9  2X9  3X5    8X9 

6XQ           4X8  8X8  8X7    5X4 

4X3     5X5  7X4  6X2    6X8 

8X2     6X9  6X9  8X4    7X4 

7X7    3X3  5X3  7x7    5X9 

8X4     5X9  8X9  5X9    5X6 

3X5     4X4  5X6  3X4    6X7 

QXQ           3X6  3X8  8X7    4X9 

5X8     6X2  7X2  9X4    8X9 

Find  the  value  of  the  following : 

(7  +  2)X9  8X(9~3)  4X(6  +  2) 

(3  +  4)X6  5X(8+1)  5X(7  +  3) 

(5  +  3)X8  4X(7-4)  3X(8-2) 

(9  +  l)X7  9X(9-3)  7X(9  +  1) 

(8-3)X6  6X(8  +  2)  6X(6-4) 

-    (8  +  2)X7  5X(9-6)  8X(7  +  2) 

(4  +  3)X5  4X(9-2)  4X(8  +  1) 

(5  +  5)  X  5  8X(5  +  2)  5X(9-6) 

(4  +  3)X8  9X(3  +  7)  6X(9-2) 

(9-2)X3  7X(3  +  2)  7X(8  +  2) 

(8-4)X9  4X(9-4)  9X(7  +  2) 

(9-5)X8  6X(8-3)  4X(5H-4) 


J 


IN    ARITHMETIC 


REVIEW    EXERCISES. 


■^    Off    T. 


Copy  and  fiiK 

1  the  vahie  of  the  J 

following  : 

2X3X4 

7  +  3X(6  +  2) 

4  +  (3X9)-5 

5X2X5 

4  +  5X(9-3) 

8+(7x2)-6 

3X2X9 

8  +  6X(4  — 2) 

7  +  (6X4)  +  2 

2X4X7 

9  +  4X(9-3) 

6  +  (8X3)+5 

4X2X8 

5  +  5X(8-5) 

6— (3X2)  +  6 

3X3X6 

4+3X(6  +  4) 

9  — (2X4)  +  5 

5X2X7 

5  +  3X(8  +  4) 

16  — (4X3)  +  5 

4X2X5 

6  +  5X(9  +  l) 

20  +  (2X6)-8 

3X3X3 

7  +  4X(8  — 3) 

17  — (3X3)  +  6 

3X3X9 

4  +  6  X  (  7—  2  ) 

25-(7x3)-4 

3X2X8 

9  +  4X(5  +  2) 

40  — (6X3)-8 

2X5X9 

2  +  3X  (6-3) 

29-(4X6)-5 

2X4X  8 

8  +  6  X  (8-6.) 

30 +  (2X3) -9 

3X2X6 

6  +  4X(9-2) 

50- (3X8) +  6 

Copy  and  find  tlie  value  of  the  i 

following : 

6X8==40+?       3X9  =  20  + 

?       3X?=20  +  1 

7X5==30  +  ?       5X8  =  33  + 

?       5x?  =  30  +  5 

6X4  =  18  +  ?       7X6  =  36  + 

?       7X?  =  37  +  5 

9X3  =  22  +  ?       5X9  =  40  + 

?       6X?  =  29  +  7 

6X8  =  39  +  ?       6X6  =  30  + 

?       4X?  =  22  +  6 

5X7  =  30  +  ?       7X7  =  50  — 

?       9X?  =  59  +  4 

6X6  =  40- 

_?       8X4  =  36- 

?       3X?=18  +  6 

7X9=70- 

_?       7X5  =  40- 

?       8X?=-59  +  5 

8X8=60  +  ?       9X6  =  60- 

?       7X?-=41  +  8 

5X9  =  51- 

-?       7X3  =  20  + 

?       6X?  =  49  +  6 

' \ )/t I 'i'/i/4" ' ' "-^y^^ ////'//. 


72  FIRST    LESSONS 

IjESSON    XIjIII. 

1.  If  Dick  had  4  rabbits,  how  many  times  could 
he  give  away  2  rabbits  to  his  companions? 

2.  Richard  sold  6 
apples,  selling  2  at 
a  time.  How  many 
times  did  he  sell  2 
apples  ? 

3,  If  William  had 
8  cents,  and  spent  it 
2  cents  at  a  time  for 

candy,    how    many   times    did    he    purchase    candy? 
How  many  2's  are  there  in  8? 

4.  How  many  times  is  2  contained  in  8? 

5.  If  you  pay  2  cents  for  a  slate-pencil,  how 
many  can  you  buy  for  10  cents?  How  many  2^s 
are  there  in  10? 

6.  How  many  times  is  2  contained  in  10? 

7.  10  is  how  many  times  2? 

Finding  how  many  times  one  number  is  contained 
in  another  is  called  Division. 

The  sign  -^  is  used  to  indicate  division.  It  is 
read  divided  by.  Thus  the  expression  8^4=2,  is 
read  8  divided  by  4  is  equal  to  2. 

8.  Read  the  following:  6-^2  =  S;  8-i-2-=4; 
10-^-2  =  5;    12-^3  =  4.      . 

9.  At  2  cents  apiece,  how  many  lemons  can  be 
bought  for  12  cents?     12-^2=? 


IN    ARITHMETIC 


73 


10.  If  a  boy  earns  2  cents  an  hour,  how  long  will 
it  take  him  to  earn  14  cents? 

11.  How  many  2's  are  there  in  16?     In  18? 

12.  If  I  have   20  cents   in   two-cent   pieces,   how 
many  pieces  have  I? 

13.  Form  the  division  tables  of  ones  and  twos. 

TABLES. 


l-f-l  =  l     6^1=   6 

2-^2  =  1    12^2-=   6 

2^1  =  2     7^1=   7 

4-1-2  =  2    14-^2=   7 

3--lr=3     8-^1==   8 

6-^2  =  S    16-^2=   8 

4^1=^4     9-^1-=   9 

8-f-2  =  4    18-^2=   9 

5-1  =  5  10-^1  =  10 

10^2  =  5    20-^-2  =  10 

3j«<C 


liESSON    XI.IV. 

1.  If  a  man  walks  3  miles  in  one  hour,  in  how 
many  hours  will  he  walk  6  miles  ?     6-^3  =  ? 

2.  If  a  boy  commits  to  memory  3  pages  of  his- 
tory in  one  day,  in  how  many  days  will  he  com- 
mit to  memory  9  pages  ?     9-^3  =  ? 

3.  At  3  cents  apiece,  how  many  lemons  can  be 
bought  for  12  cents?     12-^3  =  ? 

4.  A  w^oman  exchanged  15  pounds  of  butter  for 
cloth,  giving  3  pounds  of  butter  for  a  yard  of  cloth. 
How  many  yards  did  she  receive?     15-^3  =  ? 


74  FIRST    LESSONS 

5.  A  woman  sells  3  quarts  of  milk  each  day.     In 
how  many  days  will  she  sell  18  quarts?      18-^3  =  ? 

6.  In    one    yard   there    are    3   feet.      How   many 
yards  are  there  in  21  feet?      21h-3  =  ? 

7.  At  3  dollars  a  cord,  how  many  cords  of  Avood 
can  be  bought  for  24  dollars?     24-^-3  =  ? 

8.  If  a  boy  walks   3  miles   in   one   hour,  in  how 
many  hours  will  he  walk  27  miles  ?     27-^3  =  ? 

9.  How  many  times  is  3  contained  in  30? 

10.  At  4  dollars  a  cord,  how  many  cords  of  wood 
can  be  bought  for  8  dollars? 

11.  A   man    sold   12   sheep,   selling   4   at   a   time. 
How  many  sales  of  sheep  did  he  make?     12h-4  =  ? 

12.  16^4?     20^4=-?     24-^4  =  ?     28-^4==? 

13.  In    one    pint   there    are   4    gills.      How  many 
pints  are  there  in  32  gills?     32-^4  =  ? 

14.  In  one  bushel  there  are  4  pecks.     How  many 
bushels  are  there  in  36  pecks  ?     36  -^-  4  =  ? 

15.  In  how  many  days  will   an   engineer  earn  40 
dollars,  if  he  earns  4  dollars  a  day  ?     40  -f-  4  =  ? 

16.  Form  the  division  tables  of  threes  and  fours. 

TABLES. 


3-^3  =  1    18^3=   6 

4^4  =  1    24-^4=   6 

6-^3=^2   21-^3-=   7 

8-^4  =  2    28-^4=   7 

9-^-3=-3    24-^3-=   8 

12-^4  =  3   32-^4=   8 

12-^3  =  4   27h-3=   9 

16^4  =  4   36-^4=   9 

15-v-3  =  5   30^3  =  10 

20-^4  =  5   40^4  =  10 

I 


IN    ARITHMETIC 


75 


LESSON   XLT, 


1.  If  there  are  6  chickens  in  groups  containing 
3   each,   how   many   groups   of  chickens    are   there? 

.2.  If  a  man  earns  3  dol- 
lars a  day,  in  how  many 
days  can  he  earn  12  dol- 
lars? 

3.  How  many  seats  will 
be  required  to  seat  21  pu- 
pils, sitting  3  on  a  seat? 
21-^3  =  ? 

4.  If  a  traveling  agent 
can  earn  4  dollars  a  day, 
in  how  many  days  can  he  earn  24  dollars  at  that  rate  ? 

5.  32  is  how  many  times  4?     32-^4  =  ? 

6.  30  is  how  many  times  3?     30-^3  =  ? 

7.  A  boy  sold  5  pencils  at  4  cents  apiece,  and 
took  his  pay  in  apples  at  2  cents  apiece?  How 
many  apples  did  he  receive ?      (5X4)-^2^? 

8.  A  boy  had  25  cents.  He  bought  2  apples  at 
5  cents  apiece,  and  2  oranges  at  6  cents  apiece. 
How  many  cents  had  he  left?     (2  X  5) -f  (2  X  6)  =? 

9.  How  many  times  4  is  16?  How  many  are  2 
times  18? 

10.  A  man  sold  6  barrels  of  apples  at  3  dollars  a 
barrel,  and  took  in  exchange  some  cloth  at  2  dollars 
a  yard.      How  many  yards  did  he  receive? 

11.  How  many  times  2  acres  are  6  acres? 

12.  How  many  times  4  gills  are  40  gills? 


76  first  lessons 

Slate  Exercises. 

Copy  and  read  the  following: 

55        89        76        54        35        72         98 
79        95        84        63        55        49       100 

Copy  and  multiply  the  following : 

58696576   5   3 
7452358989 

Division  is  also  expressed  by  a  curved  line  placed 
between  numbers. 

Copy  and  divide  the  following: 

4)8      3)9      4)12      3)18      4)24      2)16 


3>»^C 


1.  If  a  boy  rides  one  mile  on  the  cars  for  5  cents, 
how  many  miles  can  he  ride  for  10  cents?     10-i-5  =  ? 

2.  If  a  boat  sails   5  miles  in  one  hour,  in  how 
many  hours  will  it  sail  15  miles?      15-^5  =  ? 

3.  At  5  dimes  apiece,  how  many  tickets  can  be 
bought  for  20  dimes?     20-^5  =  ? 

4.  In    how   many   hours   will   a   horse   travel   25 
miles,  if  he  travels  5  miles  an  hour?     25-^5  =  ? 

5.  30-^5=:?     35-^5==?     40-^5  =  ? 

6.  Fannie  attends  school  5  days  in  a  week.     How 
many  weeks  will  she  attend  if  she  is  present  45  days? 


IN     ARITHMETIC.  77 

7.  How  many  tons  of  coal  at  5  dollars  a  ton,  can 
be  bought  for  50  dollars?     50^5  =  ? 

8.  A  boy  sold  brackets  at  2  dimes  apiece,  and  got 
12  dimes.     How  many  did  he  sell?     12-v-2  =  ? 

9.  When  biscuits  are  6  cents  a  pound,  how  many 
pounds  can  be  bought  for  18  cents?     18-^6  =  ? 

10.  If  it  requires  6  yards  of  cloth  for  one  cloak, 
how  many  cloaks  can  be  made  from  24  yards  of 
cloth  ?     24  -^  6  =:  ? 

11.  How  long  will  it  take  a  boy  to  read  30  pages, 
if  he  reads  6  pages  every  day  ?     30  -^  6  ==  ? 

12.  At  6  cents  a  quart,  how  many  quarts  of  cher- 
ries can  be  bought  for  36  cents?     36-^-6  =  ? 

13.  How  many  fields  of  6  acres  each  can  be  formed 
out  of  42  acres  ?     42  ^  6  =  ? 

14.  If  there  are  6  tea-spoons  in  one  set,  how  many 
sets  will  48  tea-spoons  make  ?     48  -^  6  =  ? 

15.  If  there  are  6  pairs  of  kid  gloves  in  one  pack- 
age, how  many  packages  are  there  in  54  pairs?  How 
many  packages  are  there  in  60  pairs? 

16.  Form  the  division  tables  of  fives  and  sixes. 

TABLES. 


5^5  =  1    30-^5=   6 

6-^6  =  1    36-i-6=   6 

10-^5  =  2    35^5=   7 

12-^6=-2   42^6=   7 

15-^-5  =  3   40-^5=-   8 

18-^6  =  3    48^6=   8 

20^5=-4   45^5=   9 

24-^6  =  4    54--6=-   9 

25^5  =  5    50-^5  =  10 

30-^6  =  5    60-^6  =  10 

78  FIBST    LESSONS 


liESSON    XI.VII 


1.  If  a  man  earns  5  dollars  in  one  week,  in  how 
many  weeks  will  he  earn  50  dollars?     50-4-5  =  ? 

2.  How  many  times  can  you  take  6  cents  out  of 
a  purse  that  contains  48  cents?     48-^6  =  ? 

3.  How  many  times  3  apples  are  12  apples?  12 
^3  =  ? 

4.  How  many  calves  at  3  dollars  each,  can  be 
bought  for  18  dollars?  For  21  dollars?  For  24 
dollars?     18h-3  =  ?     21-^3  =  ?     24-^3  =  ? 

5.  There  are  4  pecks  in  1  bushel.  How  many 
pecks  are  there  in  7  bushels?     In  4  bushels? 

6.  In  32  pecks  how  many  bushels  are  there? 

7.  A  man  gave  to  each  of  4  boys  8  quails.  How 
many  quails  did  he  give  them  ?     4X8  =  ? 

8.  A  clothier  bought  10  coats  at  5  dollars  apiece, 
and  sold  them  for  6  dollars  apiece.  How  much  did 
he  gain?    (10  X  6)  -  (10  X  5)  =?    10X(6-5)  =  ? 

9.  How  many  bushels  of  potatoes  at  1  dollar  a 
bushel,  must  be  given  for  6  yards  of  cloth  at  2  dol- 
lars a  yard? 

10.  At   5  dollars   a  barrel,   how  many  barrels   of 
flour  can  be  bought  for  30  dollars?     30^5  =  ? 

11.  How    many  balls    at   6   dimes   apiece,   can   be 
bought  for  54  dimes  ?     For  30  dimes  ?     54  -^  6  =  ? 

12.  If  a  cutler  uses  18  blades,  putting  3  blades  in 
each  knife,  how  many  knives  does  he  make? 

13.  A  carman  can  draw  4  hogsheads  of  sugar  at  one 
load.     How  many  loads  will  16  hogsheads  make? 


in  arithmetic.  79 

Slate  Exercises. 

Copy  and  multiply  the  following : 

5634875321 
5387564689 

Copy  and  divide  the  following : 

6)42     5)35     3)21      2)18     3)27     4)36 


>i:«>iC 


liESSON  XI.TIII. 

•  1.  In   one  week   there   are    7   days.     How  many 
weeks  are  there  in  14  days?     14^-7  =  ? 

•  2.  In  how  many  hours  can  Carrie  solve  21  prob- 
lems, if  she  can  solve  7  per  hour  ?     21  -^-  7  =  ? 

3.  Helen  sold  her  doll  for  28  cents,  and  spent  the 
money  for  drawing-pencils,  paying  7  cents  for  each. 
How  many  pencils  did  she  buy  ?     28  -i-  7  =  ? 

4.  At  7  dollars  a  picture,  how  many  pictures  can 
be  bought  for  35  dollars  ?     35  ^  7  =  ? 

5.  If  a  fish  weighs  7  pounds,  how  many  such  fish 
will  be  needed  to  weigh  42  pounds  ?     42  -f-  7  =  ? 

6.  If  a  man  earns  7  dollars  in  one  week,  in  how 
many  weeks  will  he  earn  49  dollars  ? 

7.  If  it  requires  7  yards  of  cloth  to  make  one 
cloak,  how  many  cloaks  can  be  made  from  56  yards? 

-  8.  If  one  box  holds  7  quarts  of  nuts,  how  many 
boxes  are  required  to  hold  63  quarts  ?     63  -^  7  =  ? 


80 


FIRST    LESSONS 


9.  When    flour  is  7  dollars  a  barrel,  how  many 
barrels  can  be  bought  for  70  dollars  ?     70  -r-  7  =  ? 

10.  If  a  railroad  coacjh 
has  8  wheels,  how  many 
such  coaches  will  have  16 
wheels?     16-^8  =  ? 

11.  At  8  cents  a  yard,  how  many  yards  of  calico 
can  be  bought  for  24  cents  ?     24  ^  8  =  ? 

12.  If  a  window  requires  8  panes  of  glass,  how 
many  windows  will  32  panes  make  ?     32  -^  8  =  ? 

13.  If  there  are  8  trees  in  a  row,  how  many  rows 
of  trees  are  there  in  an  orchard  containing  40  trees? 
40-^8-=? 

14.  How  many  gallons  are  there  in  48  pints,  since 
there  are  8  pints  in  one  gallon  ?     48  -^  8  =  ? 

15.  56  divided  by  8  =  ?     64  divided  by  8  =-  ? 

16.  How  many  bins  will  be  required  to  hold  72 
bushels,  if  one  bin  holds  8  bushels?     72-^8==? 

17.  In  one  pile  of  money  there  are  8  cents.  How 
many  such  piles  are  there  in  80  cents  ?     80  h-  8  =  ? 

18.  Form  the  division  tables  of  sevens  and  eights. 


TABLES. 


7h-7=-1    42^7==   6 

8- 

-8=:1    48- 

-8=   6. 

14-^7  =  2   49-f-7=   7 

16- 

-8.-2    56- 

-8=   7 

21-^7  =  3    56-^7=   8 

24- 

-8-3    64- 

-8==   8 

28-^7  =  4   63-^7=   9 

32- 

-8  =  4   72- 

-8-:   9 

35^7  =  5    70^7  =  10 

40- 

-8=:5    80- 

-8-=10 

IN    ARITHMETIC.  81 


liESSOK  XlilX. 

1.  If  8  bushels  of  potatoes  are  needed  to  plant 
one  acre  of  ground,  how  many  acres  will  be  planted 
if  40  bushels  are  used  ?     40  -^  8  ::=  ? 

2.  If  a  blacksmith  makes  6  horseshoes  in  one  day, 
in  how  many  days  can  he  make  60  horseshoes? 

3.  If  a  man  paid  5  dollars  for  taking  one  trip  on 
the  cars,  how  many  such  trips  could  he  take  for  30 
dollars?     30^5  =  ? 

4.  In  a  school  of  56  pupils  there  are  7  pupils  in 
each  class.     How  many  classes  are  there  ?     56  -^  7  =^  ? 

5.  In  one  pint  there  are  4  gills.  How  many  pints 
are  there  in  36  gills  ?     36  -^  4  ==  ? 

6.  In  one  yard  there  are  3  feet.  How  many  yards 
are  there  in  21  feet?     In  30  feet?     In  12  feet? 

7.  If  one  ball  costs  2  dimes,  how  many  balls  can 
be  bought  for  6  dimes?  For  12  dimes?  For  18 
dimes  ? 

8.  How  many  oranges  at  5  cents  apiece  must  be 
given  for  3  dozen  of  eggs  at  10  cents  a  dozen  ? 

9.  How  many  sleds  at  3  dollars  apiece  can  be 
bought  for  27  dollars  ?     27-^3  =  ? 

10.  How  many  yards  of  calico  at  8  cents  a  yard 
must  be  given  for  10  pounds  of  maple  sugar  at  8 
cents  a  pound?     (10  X  8)^8  =  ? 

11.  If  there  are  4  pecks  in  one  bushel,  how  many 
bushels  are  there  in  40  pecks  ? 

12.  How  many  7's  are  there  in  63?     In  49? 

13.  How  many  6's  are  there  in  54?     In  48? 


82  first  lessons 

Slate  Exercises. 

Copy  and  multiply  the  following: 

687846875 
423525369 

Copy  and  divide  the  following : 

7)70      8)64      5)50      4)32      5)40      7)28 


5^8^c 


1.  If  one  dress  can  be  made  from  9  yards  of 
cloth,  how  many  dresses  can  be  made  from  18  yards? 
18-^9  =  ? 

^2.  If  a  painter  can  paint  9  boards  of  fence  in 
one  hour,  in  how  many  hours  can  he  paint  27  boards? 
27-^-9  =  ? 

3.  There  are  9  square  feet  in  1  square  yard.  How 
many  square  yards  are  there  in  36  square  feet?  In 
45  square  feet?     36-^9-=?     45-^9  =  ? 

4.  If  there  are  9  candles  in  one  pound,  how  many 
pounds  are  there  in  54  candles?     54-^-9=? 

-  5.  A  man  gave  63  bushels  of  corn  to  poor  fam- 
ilies, giving  9  bushels  to  each  family.  How  many 
families  were  relieved  ?     63  -^  9  =  ? 

6.  If  you   travel    9    miles   in    one   hour,  in    how 
many  hours  will  you  travel  72  miles?     81  miles? 
-7.  90  is  how  many  times  9  ?     90  ^  9  ==  ? 


IN    ARITHMETIC.  83 

-  8.  If  it  requires  10  pickets  to  make  one  gate, 
how  many  such  gates  can  be  made  using  20  pickets? 
20^10=-? 

9.  How    many    ten-cent    pieces    are    there    in   30 
cents?    30-^-10  =  ? 

10.  There  are  10  cents  in  one  dime.  How  many 
dimes  are  there  in  40  cents?     40-^10  =  ? 

11.  If  a  man  can  drill  10  feet  per  day,  how  many 
days  will  it  take  him  to  drill  50  feet  ?     50  ^  10  ==  ? 

12.  James  bought  a  Christmas  gift  for  60  cents, 
paying  for  it  with  ten-cent  pieces.  How  many  ten- 
cent  pieces  did  he  give  for  it  ?     60  -^  10  =  ? 

13.  How  many  hours  will  it  take  a  steamboat  to 
make  a  trip  of  70  miles,  if  it  travels  10  miles  in 
one  hour?     70-^10  =  ? 

14.  How  many  pupils,  at  10  dollars  a  term,  must 
a  teacher  instruct  to  receive  80  dollars  ?     80  -f- 10  =  ? 

15.  At  10  cents  a  pound,  how  many  pounds  of 
starch  can  be  bought  for  90  cents?     90-^10  =  ? 

16.  How  many  tens  are  there  in  100? 

17.  Form  the  division  tables  of  nines  and  tens. 

TABLES. 


9^9=1 

54^9=  6 

10-^10--1     60-^10=  6 

18^9=2 

63^9=  7 

20-^-10=2     70-^10=  7 

27^9=3 

72^9=  8 

30^10=3     80^10=-  8 

36^9=4 

81-^9=  9 

40^10=4     90^10-  9   1 

45^9=5 

90-^9=10 

50-^10=5  100-^10=10  1 

84 


FIRST    LESSON 


L^g^^^-S 


LESSOlSr   LI. 

1.  If  there  are  5  monkeys  on  one  branch  of  a 
tree,  4  on  another,  and  3  on  another,  how  many 
monkeys  are  there  on  the  tree ?     5  +  4  +  3^? 

2.  How  many  more  than  5  monkeys  are  7  monk- 
eys ?     7  —  5=-? 

3.  How  many  more  than  4  monkeys  are  8  monk- 
eys?   8  —  4==? 

4.  How  many  more  than  3  monkeys  are  9  monk- 
eys?    9  —  3=-? 

5.  If  you  have  5  apples,  how  many  more  must 
you  get  to  have  12  apples?     5  +  ?=  12. 

6.  Mary  is  6  years  old,  and  her  brother  is'  15. 
In  how  many  years  will  Mary  be  as  old  as  her 
brother  is  now?     6-\-?  =  16. 

7.  In  one  week  there  are  7  days.  How  many 
days  are  there  in  4  weeks  ?     4X7  =  ? 

8.  Into  how  many  groups  of  5  oranges  each  can 
you  divide  15  oranges  ?     15-^5  =  ? 


INARITHMETIC.  85 

9.  How    many   are    2    times    8?     4   times   8?     6 
times  8? 

10.  How  many  times  is  8  contained  in  24?  In 
40?     In  64? 

11.  If  a  cow  gives  9  quarts  of  milk  in  the  morn- 
ing, and  10  quarts  at  night,  how  many  quarts  does 
she  give  in  one  day? 

12.  George  having  20  cents,  paid  6  cents  for  candy 
and  8  cents  for  peanuts.  How  many  cents  had  he 
left? 

13.  If  one  lily  has  three  petals,  how  many  petals 
have  9  lilies? 

14.4-1-8  +  2  =  ?  9  +  7-1-3  =  ?  28  —  3  —  6  =  ? 
19_4=:?      7-1-8  —  6=? 

15.7X7  =  ?     9X8  =  ?     45-^5  =  ?     90-^10  =  ? 

16.  In  one  dime  there  are  10  cents.  How  many 
cents  are  there  in  4  dimes?     4  X  10=? 

17.  Mary  bought  4  pencils  at  5  cents  apiece,  and 
a  drawing-book  for  25  cents.  What  was  the  total 
cost  of  her  purchases? 

18.  How  many  are  6  and  8  ?  16  and  8  ?  26  and 
8?     36  and  8?     46  and  8  ?     56  and  8? 

19.  How  many  are  4  and  9?  14  and  9?  24  and 
9  ?     34  and  9  ?      44  and  9?     54  and  9  ? 

20.  Count  to  32  by  4's.     Count  to  54  by  6's. 

21.  Count  to  90  by  9's.     Count  to  72  by  8's. 

22.  Count  to  40  by  5's.     Count  to  63  by  7's. 

23.  How  many  8's  are  there  in  80  ?     80  -^  8  =  ? 

24.  How  many  7's  are  there  in  49  ?     49  ^  7  =  ? 

25.  How  many  6^s  are  there  in  54  ?     54  -r-  6  =  ? 


86  FIRST    LESSONS 

IjESSON  Hill. 

1.  Henry  takes  9  steps  in  crossing  the  room 
once.  How  many  times  will  he  cross  the  room  in 
taking  54  steps  ?     54-^9  =  ? 

2.  If  a  man  works  10  hours  in  one  day,  how 
many  hours  will  he  work  in  8  days?     8  X  10  =  ? 

-  3.  If  a  man  works  10  hours  in  one  day,  in  how 
many  days  will  he  work  100  hours?     100-^-10  =  ? 

4.  Count  to  27  by  3's.     Count  to  48  by  4's. 

5.  How  many  times  is  5  contained  in  30?  In 
45? 

6.  How  many  five-dollar  bills  will  be  required  to 
pay  for  5  tons  of  coal  at  4  dollars  a  ton  ? 

7.  A  boy  having  50  cents,  paid  30  cents  for  a 
ball  and  15  cents  for  a  bat.  How  many  cents  had 
he  left?     50-30—15=-? 

>  8.  When  clover  seed  is  8  dollars  a  bushel,  how 
many  bushels  can  be  bought  for  48  dollars?  For 
56  dollars?     48^8=?     56-^8=? 

9.  In  one  square  yard  there  are  9  square  feet. 
How  many  square  feet  are  there  in  6  square  yards  ? 

10.  36  is  how  many  times  4?  How  many  times 
6  ?     How  many  times  9  ? 

11.  24  is  how  many  times  8?  How  many  times 
6  ?     How  many  times  4  ? 

1?.  In  an  orchard  there  are  56  trees  and  7  trees 
in  a  row.     How  many  rows  are  there  ?  56  +  7  —  ? 

13.  In  one  yard  there  are  3  feet.  How  many 
feet  are  there  in  8  yards?     In  6  yards?     In  9  yards? 


I  N    ARITHMETIC. 


87 


14.  A  house  has  10  windows,  and  8  panes  of  glass 
in  each  window.  How  many  panes  of  glass  are  there 
in  the  house?     10X8  =  ? 

15.  How  many  are  6  +  4  +  5?     8  +  3  +  7? 

16.  How  many  are  12  and  5?  22  and  5?  32  and 
5?     42  and  5?     52  and  5?     62  and  5? 

17.  How  many  are  8  less  5?  18  less  5?  28  less 
5?     38  less  5?     48  less  5?     58  less  5? 

18.  Two  men  start  from  the  same  place  and  travel 
in  opposite  directions,  one  at  the  rate  of  6  miles  an 
hour,  and  the  other  at  the  rate  of  4  miles  an  hour. 
How  far  apart  are  they  in  5  hours? 


3^^C 


liESSON  lilll. 

1.  If  a  blacksmith  uses  8  nails  in  setting  one 
horseshoe,  how  many  nails  will  he  uae  in  setting 
8  horseshoes?     8X8=:=? 

2.  If  one  horse  re- 
quires 4  horseshoes,  how 
many  horseshoes  will  be 
needed  for  5  horses?     For 

6  horses?     5X4  =  ? 

3.  How  many  times  is 

7  contained    in    21  ?      In 
49?     In  56? 

4.  How  much  can  a  wagoner  earn  in  9  days,  if 
he  earns  4  dollars  per  day?     9  times  4  =  ? 


88  FIRST     TjESSONS 

5.  How   many   are   4    times    7  ?     5   times   7  ?     9 
times    7? 

6.  How   many   crows   are    5    crows,    3    crows,    6 
crows,   and    2  crows? 

7.  How  many  more  than  10  crows  are  18  crows? 

8.  How  many  more  than  6  pens  are  18  pens? 

9.  How  many  ten-dollar  bills  must  be  given  for 
8  boxes  of  handkerchiefs  at  5  dollars  a  box? 

10.6  +  7  —  4  =  ?    8  +  5  — 7  —  ?     9  +  3  — 6  =  ? 

11.  (7X4)^2==?     (8X6)H-4  =  ?     (6X6)-^9=-? 

12.  A  farmer  having  18  bushels  of  corn  sold  5 
bushels  to  one  man  and  3  to  another.  How  many 
bushels  had  he  left?     18  — (5  +  3)  =  ? 

13.  A  woman  put  20  quarts  of  strawberries  into 
cans,  putting  two  quarts  into  each  can.  How  many 
cans  did  she  use?     20h-2  =  ? 

14.  In  one  pint  there  are  4  gills.  How  many  gills 
are  there  in  7  pints  ?     7X4  =  ? 

-  15.  In  one  gallon  there  are  4  quarts.      How  many 
gallons  are  there  in  16  quarts?     16-i-4  =  ? 

16.  In  a  school-room  there  are  48  desks  arranged 
in  rows  containing  8  desks  each.  How  many  rows 
of  desks  are  there  in  the  room  ?     48  -^  8  =  ? 

17.  A  farmer  sold  some  grain  for  40  dollars,  and 
took  his  pay  in  sheep  at  5  dollars  a  head.  How 
many  sheep  did  he  receive  ?     40  ^  5  =  ? 

18.  How  many  dozens  of  eggs  at  10  cents  a  dozen 
will   pay  for  6    yards   of  calico  at  5  cents  a  yard? 

19.  If  there  are  6  forks  in  one  set,  how  many 
forks  are  there  in  9  sets?     9X6  =  ?     6X9  =  ? 


INARITHMETIC.  89 


liESSOlS^  lilV. 


-  1.  If  a  basket-maker  can  make  7  dinner-baskets 
in  one  day,  in  how  many  days  can  he  make  42  such 
baskets  ? 

2.  If  one  dining-table  has  4  legs,  how  many  legs 
have  9  such  dining-tables  ?     9X4  =  ? 

3.  What  will  be  the  cost  of  2  tops  at  10  cents 
apiece,  and  6  oranges  at  5  cents  each? 

4.  In  one  dime  there  are  10  cents.  How  many 
dimes  are  there  in  90  cents?  In  70  cents?  In  40 
cents  ? 

5.  How  many  cents  are  there  in  5  dimes?  In 
8  dimes?     In  9  dimes? 

6.  What  is  the  diiference  in  the  cost  of  6  peaches 
at  3  cents  apiece,  and  6  apples  at  2  cents  apiece? 

7.  8  +  2  +  5  =  ?     17— (8  +  4)=?     25— (5  +  2)=? 

8.  (3X2)  +  (7X3)  =  ?     27^(3X3)  =  ? 

9.  At  5  dollars  apiece,  how  many  hats  can  be 
bought  for  25  dollars? 

10.  In  one  gallon  there  are  4  quarts.  How  many 
quarts  are  there  in  4  gallons? 

-11.  If  one  fish  weighs  9  pounds,  how  many  such 
fish  will  weigh  81  pounds?     81  ^9=? 

12.  If  there  are  3  joiners'  planes  on  one  bench,  8 
on  another,  and  5  on  another,  how  many  planes  are 
there  on  the  3  benches? 

--  13.  In  a  class,  36  questions  were  answered,  each 
pupil  answering  4  questions.  How  many  pupils  were 
there  in  the  class?     36^4  =  ? 


90  FIRST   LESSONS 

14.  There  are  9  pins  in  the  pin-cushion,  12  on  the 
paper,  and  5  in  the  box.  How  many  pins  are  there 
in  all?     9  +  12  +  5  =  ? 

15.  A  tailor  earned  12  dollars  one  week,  and  15 
dollars  the  next,  and  after  paying  his  expenses  had 
8  dollars  left.  How  much  money  did  he  expend? 
(12  +  15)  — 8-=? 

16.  How  many  more  than  5  times  4,  is  30? 

17.  How  many  more  than  6  times  3,  is  24? 

18.  How  many  are  7  +  3  +  5  divided  by  3?  Di- 
vided by  5? 

19.  How  many  are  7  +  9  +  2  divided  by  6?  Di- 
vided by  3  ? 

Slate   Exercises. 

Copy  and  add  the  following : 

32235537  5 
435287626 
7445645  17 
679442442 

Copy  and  multiply  the  following : 

867987698 
595388749 

Copy  and  divide  the  following : 

6)36         8)48         8)72         9)81  7)70 

24-^6  36-^4  27-4-9  35^5 

42^6  50-^5  56^8  60-^6 


IN    AKITHMETIC 


91 


REVIEW    EXERCISES 


Find  the  value  of  the  following : 


81^9 
45^5 
36^6 
72^8 
40^5 
27^3 

18-^6 
24^4 
20-^2 
32^8 
63^7 
60-4-6 


28^4 
18-^9 
25-^5 
15^3 
18^2 
36^4 

28-^7 
30 -f- 6 
64^8 
81-^9 
20-^2 
56^8 


30-^3 
16-^-2 
45^5 
24^8 
36^9 
32^4 

35^5 
48^6 
35 -f- 7 
40^8 
32^4 
12^2 


35^5 
16^4 
27-^9 
24^3 
18^2 
64^8 

54^6 
45^5 
63^9 
35^7 

28-^4 
27^3 


Find  the  value  of  the  following 


(25  — 
(36  + 
(41  + 
(51  + 
(67  + 
(18  + 

(28  + 
(29  + 
(13  + 
(60- 
(47- 
(33  + 


5) 
6) 
7) 
3) 
5) 
3) 

4) 
7) 
3) 
4) 
2) 
3) 


(37-2) 
(49-7) 
(33  +  3) 
(  80  —  8  ) 
(  60  —  6  ) 
(33  +  7) 

(18  +  3) 
(22  +  5) 
(  43  +  6  ) 
(21+3) 
(31  +  5) 
(32  +  3) 


^5 

21^ 

^7 

36^ 

f-4 

48^ 

^-9 

32^ 

^6 

35  4 

i-8 

28^ 

f-3 

27-4 

f-9 

63^ 

f-7 

45  4 

^6 

56^ 

^-4 

49^ 

f-5 

72-^ 

28  H- 4 
21^7 
40  H- 5 
54  H- 9 
56^8 
16^2 

36^6 
46^9 
30^5 
36^4 
48-4-8 
24  H- 6 


(5  +  2) 
(7  +  2) 
(2  +  4) 
(3  +  5) 
(9-2) 
(8-4) 

(6-3) 
(7  +  2) 
(2  +  3) 
(3  +  4) 
(2  +  5) 
(6  +  3) 


92 


FIRST     LESSONS 


REVIEW    EXERCISES, 


Copy  and  find  the  value  of  the  following 


(48^8)^2 

(6+15)-^ 

-(6-3) 

4+ (16^4)— 6 

(81-^-9)-i-3 

(84-24)^ 

-(9-1) 

7+(35-^-5)— 4 

(56^7)-^4 

(7+18)-. 

-(7-2) 

8-(36-f-9)  +  2 

(70-^7)^5 

(8+28)- 

-(5+4) 

9+(81-^9)-6 

(36-h6)^3 

(9+36)- 

-(3+2) 

7+(32^4)-3 

(20^5)-^2 

(8+40)- 

-(7-1) 

3+(49-i-7)— 5 

(48-f-6)^4 

(6+30)- 

-(8-4) 

6+(64-^8)-4 

(54-^6)-^3 

(3+27)- 

^(7+3) 

5-(45-^5)+4 

(36^9) -^2 

(8+24)- 

K3+5) 

9— (42^6)— 2 

(70-^7)-^2 

(7+43)- 

^(2+3) 

8+(16^4)— 6 

(54-^9)-^3 

(9+40)- 

-(5+3) 

9+(21-^7)-6 

(64-v-8)^4 

(6+54)- 

K5+1) 

3+(64^8)-7 

(56-i-7)^2 

(8+72)- 

^(7+3) 

3+(63-^-9)— 9 

(72-^-8) -3 

(9+47)^(2+5) 

8+(60-^6)-5 

Copy  and  find  the  value  of  the  following 

45-^5=-6+  ? 

27-^  3==6+  ? 

45- 

-?=6+3 

32-f-4==5+  ? 

54-^   6-^5+? 

36- 

-?=4+2 

81-^9-=3+? 

80-f-  8=7+  ? 

72- 

-  ?=6+3 

72h-9-:6+  ? 

63-^  9=3+? 

70- 

-?=6+4 

60-^6=8+  ? 

21  :    3—4+? 

42- 

-  ?=3+4 

49^7=4+  ? 

14-f-  2=6-F? 

40- 

-?=l+3 

36-^4=3+? 

64-^  8=5+? 

54-. 

-?=4+2 

27  :  3—4+  ? 

35^  5=5+? 

48- 

-?=5+3 

164-2-=6+? 

42^  7=3+? 

35- 

-?=6+l 

24-^6-=3+  ? 

48^ 

6=2+? 

70- 

-  ?=8+2 

IN   ARITH  METIC 


93 


P^^^^^^ 


1.  Into  how  many  parts  has  one  of  the  apples  in 
the  picture  been  divided? 

2.  How  do  these  two 
parts  compare  in  size? 

3.  What  is  one  of  these 
two  equal  parts  called? 
One-half. 

4.  How  many  halves  of  the  apple  make  the  whole 
apple  ? 

5.  Into  what  number 
of  parts  is  one  of  the  pears 
divided  ? 

6.  How  do  these  three 
parts  compare  in  size?  ~  ~ 

7.  What  is  one  of  these  three  equal  parts  called? 
One-third. 

8.  What  are  two  of  these  three  equal  parts  called  ? 

9.  How  many  thirds    are 
there  in  the  whole  pear? 

10.  Into  how  many  parts 
has  one  of  the  oranges  in 
the    picture   been    divided? 

11.  How  do  these  four  parts  compare  in  size? 


94  FIEST   LESSONS 

12.  What  is  one  of  these  four  equal  parts  called  ? 
One-fourth, 

13.  What  are  two  of  the  parts  called?  What  are 
three  of  the  parts  called? 

14.  How  many  fourths  are  there  in  the  whole 
orange  ? 

One  or  more  of  the  equal  parts  of  any  thing  is 
called   a   Fraction, 

Two  numbers  written  one  above  the  other,  with 
a  line  between  them,  are  used  to  express  a  fraction. 

The  number  below  the  line  shows  the  number  of 
equal  parts  into  which  the  thing  is  divided. 

It  is  called  the  Denominator, 

The  number  above  the  line  shows  how  many  parts 
form  the  fraction. 

It  is  called  the  Numerator, 

One-half  is  therefore  expressed  thus :   \. 

One-third  is  therefore  expressed  thus:   \. 

One-fourth  is  therefore  expressed  thus:   \. 

Two-fourths  is  therefore  expressed  thus :   J. 

Three-fourths  is  therefore  expressed  thus:   J. 


Slate  Exeecises. 
Copy  and  read  the  following : 

i       *       i       I       I 


Express  in  figures  the  following : 

One-half  Two-thirds  One-fourth 

One-third  Three-fourths        Two-fourths 


IN    ARITHMETIC.  95 


U?f..  I  i-  I  i  IT  I  i  I         feli-  111  i-l  il  i  I 

1.  Draw  a  line  and  divide  it  into  5  equal  parts. 

2.  What  is  one  of  these  parts  called  ?     One-fifth. 

3.  What  are  two  of  the  parts  called?  What  are 
four  of  the  parts  called  ? 

4.  How  many  fifths  make  the  whole  line? 

5.  Draw  a  line  and  divide  it  into  6  equal  parts. 

6.  What  is  one  of  these  parts  called  ?     One-sixth. 

7.  What  are  three  of  the  parts  called  ?  What  are 
five  of  the  parts  called  ? 

8.  How  many  sixths  make  the  whole  line? 

9.  If  a  pie  is  divided  into  seven  equal  pieces,  what 
part  of  the  pie  is  one  piece  ?  Three  pieces  ?  Four 
pieces  ?     How  many  sevenths  make  the  whole  pie  ? 

10.  If  a  pound  of  candy  is  equally  divided  among 
eight  boys,  what  part  of  the  pound  will  one  boy 
receive  ? 

11.  How  many  eighths  of  it  will  four  boys  receive  ? 
Three  boys  ?     Six  boys  ? 

12.  A  miller  divided  a  barrel  of  flour  equally  among 
nine  poor  families.  What  part  of  the  barrel  of  flour 
did  he  give  to  each  family? 

13.  How  many  parts  did  he  give  to  five  families? 
To  eight  families? 

14.  If  a  dollar   is   divided    into   ten    equal   parts, 
what  is  one  of  the  parts  called  ?     What  are  foi+r  oF=-^ 
the  parts  called?    W^hat  are  ten  of  the  pac/^ called? 


(us 


96 


FIRST     LESSONS 


Slate  Exercises, 

Copy  and  read  the  following : 

1 

f 

lift 

i 

i 

i     ^     i     i 

All 

Express  in  figures  the  following: 

3  fifths  4  fifths  3  eighths 

3  sixths  2  thirds  5  eia^hths 

5  tenths  8  tenths  6  eighths 

2  ninths  7  ninths  5  sevenths 


3j#4C 


1.  Mary  had  1  half  of  a  dollar,  and  her  mother 
gave  her  1  half  of  a  dollar  more.  How  much  money 
had  she  then? 

2.  How  many  thirds  are  1  third  and  2  thirds? 

3.  If  John  gave  ^  of  an  orange  to  his  sister,  and 
I  to  his  cousin,  how  many  fourths  did  he  give  both  ? 

4.  Henry  earned  ^  of  a  dollar  in  one  day,  and  f 
of  a  dollar  the  next  day.  How  much  money  did  he 
earn  in  both  days?     How  many  fifths  are  \  and  f  ? 

5.  Jane  bought  |^  of  a  yard  of  ribbon,  and  Caro- 
line bought  I"  of  a  yard?  How  many  sixths  did 
both  buy  ?     How  many  sixths  are  |-,  |-  and  ^  ? 

6.  A  farmer  sold  |-  of  a  bin  of  wheat  to  one  man, 
and  f  to  another.     How  many  sevenths  did  he  sell? 

7.  How  many  eighths  are  f,  |-  and  J? 


I 


IN    ARITHMETIC 


97 


8.  William  bought  2J  yards  of  cloth  for  a  pair  of 
pantaloons,  f  of  a  yard  for  a  vest,  and  4^  yards  for 
a  coat.     How  many  yards  of  cloth  did  he  buy? 


9.  A  man  plowed    1  j^  acres    one    day,   and 


lA 


acres  the  next  day.     How  many  acres  did  he  plow  ? 
10.  A  laborer  bought  f  of  a  ton  of  coal  at  one 
time,  f  of  a  ton  at  another,  and  ^  of  a  ton  at  another. 
How  much  coal  did  he  buy? 


Slate  Exercises. 
Copy  and  add  the  following: 


i  +  i  +  4 


i  +  f  +  l 


l  +  f  +  l 


3j^C 


LESSON   LTIII, 


1.  Lucy  had  ^  of  a  dollar,  and  her  brother  gave 
her  :^  of  a  dollar  more.  How  much  money  did  she 
have  then  ? 

2.  How  many  halves 
of  a  dollar  are  equal  to 
one  dollar  ? 

3.  How  many  fourths 
of  a  dollar  are  equal  to 
one  dollar? 

4.  How  many  fourths  of  a  dollar  are  equal  to 
one-half  of  a  dollar?     How  many  fourths  are  there 


ini? 


9 


1  -  -  ■ 

98  FIRST    LESSONS 

5.  How  many  fourths  of  a  dollar  are  there  in  ^ 
and  J  of  a  dollar?     How  many  fourths  in  ^  and  ^? 

6.  Draw    two    lines    of 
the  same  length. 

7.  Divide  the  first  line 
into  2  equal  parts. 

8.  Divide  the  second  line  into  6  equal  parts. 

9.  What  is  one  part  of  the  first  line  called  ? 

10.  What  is  one  part  of  the  second  line  called? 

11.  What  are  three  parts  of  the  second  line  called? 

12.  How  do  three  parts  of  the  second  line  compare 
in  length  with  one  part  of  the  first  line  ? 

13.  How  many  sixths  of  a  line  are  equal  to  one- 
half  of  a  line  ? 

14.  How  many  sixths  are  there  in  ^  and  ^?     How 
many  sixths  are  there  in  J  and  |-  ?     In  ^  and  f  ? 

15.  How  many  eighths   are   equal   to  one-fourth? 
Hcfw  many  eighths  are  there  in  ^  and  f  ? 

■    16.  Mary  bought  2^  yards  of  lace  one  day,  and  2^ 
yards  the  next  day.     How  many  yards  did  she  buy  ? 

17.  John  bought  2^  pounds  of  raisins,  and  Joseph 
bought  3f  pounds.     How  many  pounds  did  they  buy  ? 

18.  How  many  ninths  are  ^  and  ^?     f  and  |^? 

19.  How  many  eighths  are  ^  and  f  ? 

Slate  Exercises. 
Copy  and  add  the  following : 

i+i+i         i+l+l         i+i+i 
*+i+f         i+i+i         i+l+A 


IN     ARITHMETIC.  99 

liESSOlS^    I.IX. 

1.  Henry  had  3  fourths  of  an  orange,  but  gave 
1  fourth  of  it  to  his  cousin.     How  much  had  he  left? 

2.  If  a  boy  had  f  of  a  pound  of  candy,  but  gave 
^  of  it  away,  how  much  had  he  left?     -|  —  i  =  ? 

3.  If  I  have  f  of  a  dollar,  and  spend  ^  of  a  dol- 
lar, what  part  of  a  dollar  will  I  have  left? 

4.  A  girl  having  -j^  of  a  dollar,  paid  ^^  of  a 
dollar  for  thread.     How  much  had  she  left? 

5.  From  ^  take  ^.     From  |^  take  ^. 

6.  If  Julia  divides  a  loaf  of  cake  into  8  equal 
parts,  and  gives  away  -|  of  it,  how  many  eighths 
will  she  have  left? 

7.  A  man  chopped  f  of  a  cord  of  wood  in  the 
forenoon,  and  f  of  a  cord  in  the  afternoon.  How 
much  more  did  he  chop  in  the  afternoon  than  in  the 
forenoon  ?     f  —  f  ^^  ? 

8.  Gilbert  owns  f  of  a  boat,  and  Carl  the  re- 
mainder.    What  part  does  Carl  own? 

9.  Oscar  bought  a  pair  of  skates  for  -^^  of  a  dol- 
lar, and  sold  them  for  -^-q  of  a  dollar.  What  part 
of  a  dollar  did  he  lose?     -^  —  to"^^^ 

10.  How  much  more  than  |^  of  a  pound  is  f  of  a 
pound?     f  — f  =  ? 

11.  In  a  school  f  of  the  pupils  are  girls,  and  the 
rest  are  boys.     What  part  of  the  school  is  boys  ? 

12.  How  many  more  than  3^  are  8^  ? 

13.  A  grocer  having  lOf  pounds  of  butter,  sold  4 
pounds  of  it.     How  much  had  he  left? 


100  FIRST     LESSONS 

14.  A  tailor  had  12|-  yards  of  cloth,  and  sold   3f 
yards.     How  many  yards  had  he  left? 

Slate  Exercises. 
Copy  and  subtract  the  following : 

4 1  7  2.  6. 3  4  1 

•6  "6  ¥  8  9  9  Z 5" 

6A-¥o       H-H        8f-2J        9f-3f 


3j^C 


1.  Into  how  many  parts  is  the  first  melon  in  the 
picture  cut?     How  do  the  parts  compare  in  size? 

2.  Into  how  many  equal 
parts  is  each  of  the  halves  of 
the  second  melon  cut? 

3.  How  many  such  parts 
are  there  in  the  two  halves^ 
or  the  whole  melon? 

4.  What  are  these- parts  called? 

5.  How  many  sixths  are  there  in  one-half? 

6.  From  -l-  subtract  ^.     From  ^  subtract  f. 

7.  Draw  a  line  and   divide  it  into  3  equal   parts. 

8.  Draw   another   line  of  the    same   length,  and 
divide  it  into  3  equal  parts. 

9.  Divide  each  part  of  the  second  line  into  3  equal 
parts. 

10.  How  many  of  these  smaller  parts  are  there  in 
the  whole  line?     What  are  these  parts  called? 


I 


IN    ARITHMETIC.  101 

11.  How  many  ninths  are  there  in  one  third? 

12.  How  many  ninths  are  there  in  two  thirds? 

13.  From  ^  of  an  orange  take  f  of  an  orange. 

14.  Belle  having  f  of  a  yard  of  velvet,  gave  away 
I  of  a  yard.     How  much  had  she  left? 

15.  A  grocer  who  had  ^  of  a  barrel  of  beans,  sold  f 
of  a  barrel.    What  part  of  a  barrel  did  he  have  left? 

16.  How  many  tenths  of  a  dollar  are  there  in  one- 
fifth  of  a  dollar?     In  two-fifths? 

17.  From  f  of  an  hour  take  -^  of  an  hour. 

18.  A  milliner  having  4f  yards  of  silk,  used  2-| 
yards.     How  many  had  she  left? 

Slate  Exercises. 
Copy  and  subtract  the  following: 


l-i 

f-f 

l-i 

f-A 

^-^ 

H-H 

5i-2i 

71-lA 

^-^ 

5i-2i 

^-^ 

6i-6A 

5^#<C 


IiESSO:N^    I.XI. 


1.  Clara  had  a  yard  of  cambric.  She  gave  Grace 
J  of  it,  and  Lizzie  f  of  it.  How  much  had  she 
left? 

2.  A  bushel  of  wheat  was  divided  among  three 
persons.  One  received  ^  of  it,  another  i  of  it,  and 
the  third  the  rest.  What  part  did  the  third  per- 
son receive? 


102  FIRST     LESSONS 

3.  George  paid  ^  of  a  dollar  for  a  slate,  |  of  a 
dollar  for  a  reading-book,  and  ^  of  a  dollar  for  a 
writing-book.     What  did  he  pay  for  all? 

4.  A  man  dug  f  of  a  ditch  one  day,  ^  of  it  the 
second  day,  and  the  rest  of  it  the  third  day.  What 
part  of  the  ditch  did  he  dig  the  third  day  ? 

5.  From  ^  +  |  take  i.     From  ^  +  ^  take  ^. 

6.  From  f  +  ^  take  ^.     From  f  +  |-  take  |-. 

7.  To  the  difference  between  ^  and  f  add  ^. 

8.  To  the  difference  between  -^-^  and  f  add  ^. 

9      24-i_l-3  2—9        l-|-2._i_2. 1—9 

10.  Peter  had  f  of  a  dollar.  His  father  gave  him 
-^  more,  and  his  mother  gave  him  enough  to  make 
the  dollar.     How  much  did  his  mother  give  him? 

11.  James  paid  ^  of  a  dollar  for  a  book,  -J  of  a 
dollar  for  a  slate,  and  f  of  a  dollar  for  writing-paper. 
How  much  did  he  pay  for  all?    i  +  i  +  f^? 

12.  How  much  more  did  he  pay  for  the  book  than 
for  the  slate?     i— ^=? 

14.  William  owns  f  of  a  sled,  and  his  brother  the 
remainder.  What  part  of  the  sled  does  his  brother 
own? 

Slate  Exercises. 

Find  the  value  of  the  following : 

H  +  H       3f  +  5i       4I  +  6A  8|  +  10i 

6|-5f       8^-4f       H-Si^  m-H 

2|  +  3^       5|  +  3^       6}  +  2f  5t  +  3i 

H-H       9f-4i     8^-4^  6^-3^ 


IN     ARITHMETIC.  103 

liESSOlS^   liXII. 

1.  If  one  pint  of  peanuts  costs  1  half  of  a  dime, 
what  will  5  pints  cost  ?     5  times  |^  =  ? 

2.  If  one  yard  of  cloth  costs  2  fourths  of  a  dollar, 
what  will  3  yards  cost?     3  times  f  =  ? 

3.  If  it  takes   2  eighths  of  a  yard  of  lace  for  one 
veil,  how  much  lace  will  it  take  for  3  veils  ? 

4.  How  many  sevenths  are  2  times  2  sevenths  ? 

5.  How  many  ninths  are  3  times  3  ninths  ? 

6.  3  times  |  ==  ?     7  times  f  =  ?     4  times  |  =  ? 

7.  If  a  man  earns  2  dollars  in  one  day,  how  much 
will  he  earn  in  1  half-day  ?     ^  of  2  =  ? 

8.  If  1  yard  of  cloth  costs  9  dollars,  what  will  1 
third  of  a  yard  cost  ?     ^  of  9  =  ? 

9.  When  coal  is  7  dollars  a  ton,  what  will  1  seventh 
of  a  ton  cost  ?     What  will  2  sevenths  of  a  ton  cost  ? 

10.  Mary  is  15  years  old,  and  her  sister  is  2  fifths  as 
old.     How  old  is  her  sister?     15  X  f  =  ? 

11.  6  multiplied  by  ^=^2    By  |?     By  ^?     By  |? 

12.  10  multiplied  by  |  =  ?   By|?     Byf?     By  ^L? 

13.  A  boy  having  20  pennies  gave  ^  of  them  to  one 
boy,  and  ^  of  them  to  another.  How  many  did  he 
give  to  both  ?     How  many  had  he  left  ? 

14.  If  a  pound  of  cinnamon  costs  21  cents,  what 
will  ^  of  a  pound  cost?    What  will  |^  of  a  pound  cost? 

15.  If  a  barrel  of  sugar  is  worth  25  dollars,  what  is 
^  of  it  worth  ?     What  are  f  of  it  worth  ? 

16.  What  is  the  product  of  f  multiplied  by  6?  6 
multiplied  by  f  ? 


104  fikst   lessons 

Slate  Exercises. 
Find  the  value  of  the  following : 


6  times  j-, 

or    f  X  6. 

|X5. 

iX2 

5  times  f , 

or    1  X  5. 

iX5. 

iX5 

f     of     6, 

or     6  X  |. 

8X|. 

6X| 

1     of   12, 

or  12  X  f . 

9X1. 

12Xf 

^>^c 


LESSON  liXIII 


1.  At  |-  of  a  dollar  each,  how  many  books  can  be 
bought  for  1  dollar?  How  many  times  is  ^  contained 
in  1? 

2.  At  2  fifths  of  a  dollar  per  yard,  how  much  cloth 
can  be  bought  for  4  fifths  of  a  dollar?  How  many 
times  are  f  contained  in  |^? 

3.  If  a  boy  can  earn  2  eighths  of  a  dollar  per  day, 
how  long  will  it  take  him  to  earn  6  eighths  of  a  dol- 
lar?    How  many  times  are  f  contained  in  f? 

4.  If  a  man  can  mow  f  of  an  acre  in  one  hour, 
how  long  Will  it  take  him  to  mow  j-  of  an  acre?  How 
many  times  are  f  contained  in  -f^? 

5.  A  boy  having  f  of  a  pound  of  candy,  divided 
it  equally  among  his  playmates,  giving  to  each  f  of 
a  pound.     How  many  playmates  had  he  ? 

6.  A  grocer  having  ^  of  a  barrel  of  vinegar,  sold 
3^  of  a  barrel  each  day  until  it  was  all  sold.  In  how 
many  days  did  he  sell  it? 


IN    AKITHMETIC.  105 

7.  How  many  times  are  -^  contained  in  3^,  or 
what  is  the  vahie  of  9  tenths  -^  3  tenths? 

8.  How  many  times  are  -^  contained  in  3^,  or 
what  is  the  value  of  it  "^  IT  ^ 

9.  How  long  will  it  take  a  boy  to  earn  ^  of  a 
dollar,  by  earning  ^  of  a  dollar  per  day?  How 
many  times  are  -fy  contained  in  3^  ?     -fs  "^  A  ^^  ^ 

10.  How  many  times  are  f  contained  in  ^?    3^  in 
M?    A  in  if?    A  in  if?    ^  in  H? 

11.  How  long  a  time  will  be  required  to  fill  a  cis- 
tern, if  ^  of  it  is  filled  every  hour  ?     lor^-^-^  =  ? 

Slate  Exercises. 
Find  the  value  of  the  following : 

¥ 
2 


3>®^C 


liESSOK   I.XIV. 

1.  If  William  divides  4  oranges  equally  between 
his  2  sisters,  how  many  will  each  receive  ? 

2.  What  is  one-half  of  4  cents  ?     What  is  one-half 
of  4? 

3.  By  what  number  do  you  divide  to  find  one-half 
of  any  number  ? 

4.  How  many  pears  is  1  third  of  3  pears  ? 

5.  How  many  pears  are  2  thirds  of  3  pears? 


^1- 

¥^*- 

¥^l- 

¥-^l 

^i- 

¥^i- 

¥^f- 

¥-^1 

H- 

i^h 

8^1. 

7-^1 

106  FIRST    LESSONS 

6.  By  what  number  do  you  divide  to  find  one- 
third  of  any  number?  How  do  you  find  2  thirds 
of  a  number? 

7.  How  many  roses  are  one-half  of  8  roses? 

8.  If  a  woman  divides  5  loaves  of  bread  equally 
between  5  persons,  what  part  will  each  person  receive  ? 

9.  How  many  loaves  are  3^  of  5  loaves?  f  of  5 
loaves?    f  of  5  loaves? 

10.  How  is  ^  of  a  number  found  ?     f  of  a  number  ? 

11.  If  14  marbles  are  equally  divided  between  2 
boys,  how  many  marbles  does  each  boy  receive? 

12.  How  many  are  ^  of  14  ?    How  many  are  ^  of  14? 

13.  One-fourth  of  20  cents  is  how  many  cents? 

14.  By  what  number  do  you  divide  to  find  one- 
fourth  of  any  number  ? 

15.  A  man  shot  12  pigeons  and  sold  ^  of  them. 
How  many  had  he  left? 

16.  A  boy  saAv  18  fowls,  |-  of  which  were  white. 
How  many  were  white  ? 

17.  A  boy  having  40  cents,  paid  4  of  his  money  for 
pencils  and  -^  of  it  for  paper.  How  much  did  he 
have  left? 

18.  A  farmer  sold  7  bushels  of  wheat  for  28  dollars. 
What  did  he  receive  for  one  bushel? 

19.  How  many  bushels  are  ^  of  28  bushels? 

20.  How  many  bushels  are  ^  of  28  bushels? 

21.  What  is  J^  of  20?     What  is  |  of  56  ? 

22.  If  25  dollars  is  divided  equally  among  5  men, 
what  part  of  the  money  will  each  receive?  How 
much  will  each  receive? 


IN     ARITHMETIC. 


107 


^ 


NGTATiONA  NUMERATION 


tif 


LESSOIS^   I.XV. 


A  single  thing  is  called  a  Unit, 

How  many  units  make  one  ten?     Two  tens? 


Copy  and  read 

10  12 

16  64 


27 
73 


35 


42 

90 


59 
99 


4.  Express  in  figures  the  following  : 

Ten.  Forty-eight.  Eighty -five. 

Thirteen.  Sixty-fi3ur.  Ninety. 

Twenty-five.  Seventy-nine.  Ninety-three. 

Thirty-two.  Eighty-one.  Ninety-nine. 


5.  Express  in  figures  the 

One  ten,  no  units. 
Five  tens,  six  units. 
Six  tens,  four  units. 
Two  tens,  seven  units. 
Seven  tens,  one  unit. 
Three  tens,  five  units. 
Eight  tens,  six  units. 
Foui;  tens,  five  units. 
Nine  tens,  nine  units. 


following : 

One  ten,  one  unit. 
Five  tens,  two  units. 
Six  tens,  six  units. 
Two  tens,  one  unit. 
Seven  tens,  three  units. 
Three  tens,  four  units. 
Eight  tens,  one  unit. 
Four  tens,  six  units. 
Nine  tens,  one  unit. 


108  FIRST    LESSONS 

6.  When  two  figures  are  written  side  by  side  what 
does  the  one  at  the  right  represent?  What  does  the 
one  at  the  left  represent? 

7.  How  many  tens  and  units  in  ninety-nine  ? 

8.  If  one  is  added  to  the  9  units,  what  is  the  result? 

9.  How  many  are  9  tens  and  1  ten  ? 
10.  How  many  tens  make  one  hundred  ? 


11.  Copy 

and  reac 

1: 

100 

104 

108 

116 

138 

149 

157 

168 

173 

123 

188 

199 

205 

316 

423 

216 

304 

229 

12.  Express  the  following  in  figures ; 

One  hundred,  two  tens,  and  five  units. 
Four  hundreds,  five  tens,  and  no  units. 
Seven  hundreds,  five  tens,  and  six  units. 
Eight  hundreds,  nine  tens,  and  one  unit. 
Three  hundreds,  nine  tens,  and  eight  units. 
Five  hundreds,  three  tens,  and  seven  units. 

Two  hundred.  Nine  hundred. 

Two  hundred,  forty.  Nine  hundred,  forty. 

Eight  hundred,  five.  Six  hundred,  seventy. 

Three  hundred,  fifty.  Five  hundred,  eighty. 

Three  hundred,  forty.  Five  hundred,  twenty. 

Five  hundred,  ninety.  Seven  hundred,  thirty. 

13.  When  three  figures  are  written  side  by  side, 
what  does  the  one  at  the  right  represent?  ^  The  one 
next  to  it?     The  one  at  the  left? 


IN  . 

A.IIITHMETIC 

.  Copy  and  read 

: 

314    268 

572 

681 

372 

465 

200    2G0 

350 

580 

673 

856 

371    426 

842 

730 

307 

406 

184    755 

862 

985 

422 

999 

109 


15.  Express  in  figures  the  following: 

Two  hundred,  ten. 
Five  hundred,  fifty. 
Two  hundred,  forty. 
Seven  hundred,  five. 
Eight  hundred,  four. 
Nine  hundred,  fifteen. 
Five  hundred,  sixteen. 
Eight  hundred,  twelve. 
Five  hundred,  fifty-five. 
Four  hundred,  sixty-six. 
Nine  hundred,  forty -five. 
Six  hundred,  forty-seven. 
Eight  hundred,  fifty-four. 
Seven  hundred,  forty-one. 
Nine  hundred,  ninety-nine. 
Eight  hundred,  sixty-three. 
Three  hundred,  ninety-nine. 
Seven  hundred,  twenty-nine. 

The  method  of  expressing  numbers  by  figures  is 
called  the  Arabic  notation. 

The  method  of  reading  numbers  is  called  NumeV" 
ation. 


110  FIRST     LESSONS 


LESSOIS^   I.XTI. 

1.  If   1    be   added   to   nine   hundred  ninety-nine, 
how  many  hundreds  will  there  be? 

2.  To  what  are  10  hundreds  equal  ?     One  thousand, 

3.  One  thousand  is  expressed  thus:    1^000, 

4.  Copy  and  read  the  following : 

1,000  1,004  1,016  1,323  1,548 
2,000  2,159  3,872  5,625  7,822 
8,465        6,372        4,189         9,786         9,999 

5.  Express  in  figures  the  following: 

Seven  thousand,  two  hundred,  fifty-six. 
Nine  thousand,  nine  hundred,  ninety-five. 
Five  thousand,  three  hundred,  twenty-eight. 

6.  How  many  are  9  thousand  and  1  thousand? 

7.  Ten  thousand  is  expressed  thus:    10^000, 

8.  Copy  and  read  the  following: 

10,000  18,000  '  22,005  35,012 
87,482     96,856     13,729     88,543 

9.  Express  in  figures  the  following: 

Ninety  thousand,  nine  hundred,  fifty-six. 
Eighty -four  thousand,  five  hundred,  forty. 
Seventy-five  thousand,  eight  hundred,  fifty. 
Fifty-three  thousand,  two  hundred,  twenty. 
Eighty  thousand,  seven  hundred,  forty-four. 
Ninety  thousand,  nine  hundred,  ninety-nine. 


IN    ARITHMETIC.  Ill 

10.  How  many  are  90  thousand  and  10  thousand? 

11.  One    hundred     thousand     is     expressed     thus: 
100,000. 


liESSON   I.XTII. 

1.  Copy  and  read  the  following: 

"     100,000         120,000         562,000        159,725 
540,805         723,016         986,784         684,379 

2.  What  do  the  three  figures  at  the  right  repre- 
sent?     Units,  tens,  and  hundreds, 

3.  What  do  the  three   figures   at   the  left  repre- 
sent?     Units,  tens,  and  hundreds  of  thousands. 

4.  A  group  of  figures  containing  the  units,  tens, 
and  hundreds  of  any  denomination  is  called  a  Period. 

5.  How  many  periods   are   there   in   the   number 
132,654? 

6.  What  is  the  denomination  of  the  first  period? 

7.  What  is  the  denomination  of  the  second  period? 

8.  Copy  and  read  the  following: 


354,728 

639,955 

845,762 

876,953 

423,872 

635,476 

82,675 

400,800 

8,005 

264,361 

315,008 

216,040 

9.  How  many  figures  must  there  be  in  a  period? 
10.  How  are  the  periods  separated  from  each  other  ? 


112  FIEST    LESSONS 

Express  in  figures  the  following: 

11.  Two  hundred  eight  thousand,  five  hundred  sev- 
enty-four. 

12.  Seven  hundred  fifty-four  thousand,  two  hundred 
twenty-five. 

13.  Eight  hundred  sixty-three  thousand,  four  hun- 
dred eighty-nine. 

14.  Eight  hundred  sixty-five  thousand,  three  hun- 
dred thirty-seven. 

15.  Eighty-four  thousand,  five  hundred  eighty-four. 

16.  Nine  hundred  thirty-three  thousand,  six   hun- 
dred twelve. 

17.  Three  hundred  thousand,  six  hundred. 

18.  Eight  hundred  ninety-four  thousand,  six  hun- 
dred twenty-four. 

19.  Five  hundred  eighty  thousand,  seven  hundred 
ninety-seven. 

20.  Three    hundred    eighty-nine    thousand,    seven 
hundred  eighty-one. 

21.  Seven  hundred  eighteen  thousand,  nine  hundred 
eighty-seven. 

22.  Six  hundred  thousand,  one. 

23.  Six  hundred  twenty-four  thousand,  three  hun- 
dred twenty-nine. 

24.  Eight  hundred  thirty-nine  thousand,  five  hun- 
dred sixteen. 

25.  Nine  hundred,  thirty-five  thousand,  eight  hun- 
dred twenty-six. 

26.  Nine  hundred  sixty-eight  thousand,  nine  hun- 
dred thirty-seven. 


IN    ARITHMETIC.  113 


-^=7^^ 


LESSON   I.XVIII. 

1.  Helen  solved  6  examples,  Martha  solved  5, 
and  Jennie  solved  9.  How  many  examples  did 
they  all  solve  ? 

2.  How  many  goblets  are  3  goblets,  8  goblets, 
and  9  goblets? 

3.  James  learned  5  lessons  on  Monday,  6  lessons 
on  Tuesday,  and  3  lessons  on  Wednesday.  How 
many  lessons  did  he  learn  in  the  three  days? 

4.  How  many  marbles  are  5  marbles,  4  marbles, 
6  marbles,  and  2  marbles? 

5.  After  spending  2  cents  for  a  slate-pencil  and  5 
cents  for  a  lead-pencil,  James  had  5  cents  left.  How 
much  had  he  at  first? 

6.  How  many  dollars  are  10  dollars  and  8  dollars? 

DEFINITIONS. 

The  process  of  finding  one  number  that  is  equal 
to  two  or  more  numbers  is  called  Addition, 

The  result  in  addition  is  called  the  Sum, 

The  Sign  of  Addition  is  an  upright  cross :  -f- , 
called  plus. 

The   Sign  of  Equality  is  two  short  horizontal 
lines:  =. 
10 


114  FIRST    LESSONS 

1.  What  is  the  sum  of  5,  4,  7,  and  6  ? 

PROCESS.  Explanation.  —  For  convenience  the  numbers 

n  to  be  added   are  arranged  so  that  tliey  stand   in  a 

column. 

"*  We  begin  at  the  bottom  to  add,    thus:    6,  13, 

7  17,  22,  and  write  the  sum  beneath. 

/»  Hence,  the  sum  is  22. 

In  adding  say  6,  13,  17,  22,  instead  of   6  and  7 

22  are  13  and  4  are  17  and  5  are  22. 

Slate  Exercises. 
Copy  and  add  the  following : 


(2.) 

(3.) 

(4.) 

(5.) 

(6.) 

4 

5 

6 

8 

3 

2 

6 

5 

2 

2 

3 

3 

3 

3 

5 

5 

4 

2 

3 

1 

7.  William  shot  6  squirrels,  Henry  shot  8,  John 
shot  5,  and  James  shot  7.  How  many  squirrels  did 
they  shoot? 

8.  Oscar  owned  4  cows,  Herbert  owned  5,  George 
owned  3,  and  Clarence  owned  6.  How  many  cows 
did  the  four  boys  own? 

9.  A  merchant  received  5  boxes  of  oranges  one 
day,  6  the  next,  and  4  the  next.  How  many  boxes  of 
oranges  did  he  receive? 

10.  A  farmer  sold  6  cords  of  wood  to  one  man,  3 
cords  to  another,  8  to  another,  and  2  to  another. 
How  many  cords  of  wood  did  he  sell  ? 


IN    ARITHMETIC.  115 


Slate  Exercises. 
Copy  and  add  the  following  : 


(11.) 

(12.) 

(13.) 

(14.) 

(15.) 

4 

6 

3 

4 

6 

7 

5 

6 

7 

2 

8 

7 

9 

2 

3 

2 

8 

2 

3 

9 

3 

5 

6 

5 

3 

4 

1 

2 

4 

2 

3j^C 


liESSON   I.XIX. 

1.  What  is  the  sum  of  217,  853,  and  365? 

PROCESS.  Explanation. — For  convenience  the  num- 

o  1  Y  bers  to  be  added  are  arranged  so  that  units 

Q  ^  ey  stand  under  units,  and  tens  under  tens,  etc. 

Beginning  at  tiie  right  hand,  each  column 

*^  o  "  '  is  added  separately. 

2^  z|.  3  5  Thus,  5  +  3-1-7  =  15,  the  sum  of  the  units. 

15  units  are  equal  to  1  ten  and  5  units.    The  5 

is  written  under  the  column  of  units,  and  the  1  is  reserved  to  add 

with  the  tens. 

1  reserved  +6  +  5  +  1=13,  the  sum  of  the  tens.  13  tens  are 
equal  to  1  hundred  and  3  tens.  The  3  is  written  under  the  column 
of  tens,  and  the  1  is  reserved  to  add  to  the  column  of  hundreds. 

1  reserved  +3  +  8  +  2  =  14,  the  sum  of  the  hundreds.  14 
hundreds  are  equal  to  1  thousand  and  4  hundreds,  which  are  written 
in  thousands'  and  hundreds'  places  in  the  sum. 

In  adding,  name  results  only.  Thus,  instead  of  saying,  5  and  3 
are  8  and  7  are  15,  say  5,  8,  15. 


116  first   lessons 

Slate  Exercises. 
Copy  and  add  the  following : 


(2.) 

(3.) 

(4.) 

(5.) 

678 

852 

338 

852 

153 

365 

466 

738 

261 

472 

^53 

645 

(6.) 

(7.) 

(8.) 

(9.) 

235 

512 

832 

893 

415 

416 

142 

416 

268 

304 

624 

842 

317 

497 

615 

249 

10.  A  man  traveled  250  miles  by  railroad,  325  by 
steamboat,  and  190  by  stage.  How  many  miles  did 
he  travel  ? 

11.  What  is  the  sum  of  three  thousand  five  hundred 
twenty-six,  eight  thousand  one  hundred  twelve,  six 
thousand  nine  hundred  eighteen? 

12.  A  butter-buyer  bought  326  pounds  of  butter 
from  one  dairy,  518  pounds  from  another,  and  168 
pounds  from  another.  How  many  pounds  of  butter 
did  he  buy? 

13.  Find  the  sum  of  six  hundred  seventy-nine, 
three  hundred  twenty-eight,  and  fourteen. 

14.  Three  persons  deposited  money  in  a  bank.  The 
first  put  in  192  dollars,  the  second  466  dollars,  and 
the  third  825  dollars.  How  much  money  did  they 
deposit  ? 


I 


IN     ARITHMETIC.  117 

15.  A  man  paid  400  dollars  for  a  span  of  horses, 
150  dollars  for  a  carriage,  and  75  dollars  for  a  harness. 
How  much  money  did  he  pay  for  all  ? 

Copy  and  add: 

(16.)  (17.)  (18.) 

6,231  27,638  25,789 

1,354  13,925  32,644 

4,872  53,164  58,793 

3,125  41,538  62,461 

3,258  31,604  58,261 

4,123  58,643  21,469 


(19.) 

(20.) 

(21.) 

6,843 

13,462 

46,845 

2,754 

26,541 

27,891 

6,281 

32,716 

84,263 

4,156 

42,683 

38,419 

7,123 

94,275 

32,981 

8,142 

24,239 

19,497 

(22.) 

(23.) 

(24.) 

4,265 

68,465 

48,634 

3,789 

31,892 

31,299 

4,573 

47,468 

87,109 

4,684 

39,210 

46,296 

4,591 

40,009 

37,415 

8,743 

32,567 

45,984 

4,268 

26,849 

51,846 

5,745 

45,265 

74,695 

118 


FIRST    LESSONS 


SUBTRACTION 


liESSOI^    I.XX 


1.  Herbert  earned  19  dollars  and  gave  7  dollars  for 
a  coat.     How  much  had  he  left? 

2.  Mary  painted  18  pictures  and  sold  6  of  them. 
How  many  had  she  left? 

3.  If  a  man  earns  15  dollars  a  week  and  uses  8 
dollars,  how  many  dollars  will  he  have  left? 

4.  A  grocer  having  22  pounds  of  lard,  sold  11 
pounds  of  it.     How  many  pounds  had  he  left? 

5.  William  had  12  marbles,  but  gave  away  5  of 
them.     How  many  had  he  left? 

6.  25  pencils  are  how  many  more  than  10  pencils? 

7.  From  a  piece  of  cloth  containing  22  yards,  16 
yards  were  cut.     How  many  yards  remained? 

8.  From  a  cistern  containing  40  gallons  of  water, 
10  gallons  were  drawn  out.  How  many  gallons  re- 
mained ? 

9.  There  are  24  pupils  in  a  school,  of  whom  13  are 
boys.     How  many  are  girls? 

10.  One  piece  of  cloth  contained  26  yards,  and 
another  contained  13  yards.  How  many  yards  more 
were  there  in  the  larger  piece  ? 

11.  A  farmer  who  had  23  horses,  sold  11  of  them. 
How  many  horses  had  he  left? 


IN    ARITHMETIC.  119 

DEFINITIONS. 

The  process  of  finding  the  difference  between  two 
numbers  is  called  Subtraction. 

The  greater  of  the  two  numbers  is  called  the 
Minuend. 

The  lesser  of  the  two  numbers  is  called  the  Sub- 
trahend. 

The  result  obtained  by  subtracting  is  called  the 
Meniainder  or  Difference, 

The  Sign  of  Subtraction  is  a  short  horizontal 
line  :  — ,  called  minus. 

1.  From  768  subtract  425. 

PKOCESS.  Explanation, — For  convenience  the  less 

-  ^  „  number   is  written   under  tlie  greater,  units 

under  units,  tens  under  tens,  etc. 
4  2  5  Beginning  at  the   right  hand,  each  figure 

3  4  3  ^^  ^^^^  subtrahend  is  subtracted  from  the  cor- 

responding figure  of  the  minuend. 
8  units  minus  5  units  equal  3  units,  which  are  written  under 
the  units. 

6  tens  minus  2  tens  equal  4  tens,  which  are  written  under  the 
tens. 

7  hundreds  minus  4  hundreds  equal  3  hundreds,  which  are 
written  under  the  hundreds.     Hence  the  remainder  is  343. 

Slate  Exercises. 
Copy  and  subtract  the  following : 


(2.) 

(3.) 

(4.) 

(5.) 

(6.) 

635 

876 

957 

543 

665 

421 

453 

835 

320 

543 

120  FIUST    LESSONS 

I.ESSOX    LXXI. 

1.  From  7425  subtract  2536? 

PROCESS.  Explanation.  —  For  convenience  the 

.,.         ,        ^  .  f^  r  less  number  is  written  under  the  greater. 

Minuend         7425  .^         ,  .^,  ,,        ,,/ 

units  under  units,  tens  under  tens,  hundreds 
Subtrahend    2536  under  hundreds,  etc. 

Remainder     4  8  8  9  Beginning  at  the  right  hand,  each  fig- 

ure of  the  subtrahend  is  subtracted  from 
the  corresponding  figure  of  the  minuend. 

Since  6  units  can  not  be  subtracted  from  5  units,  1  ten  is  united 
with  the  5  units.  1  ten  is  equal  to  10  units.  10  units  and  5  units 
are  15  units.  6  units  from  15  units  leave  9  units.  The  9  is  writ- 
ten in  units'  place. 

Since  1  of  the  tens  was  united  with  the  units,  there  is  but  1  ten 
left.  Because  3  tens  can  not  be  subtracted  from  .1  ten,  1  hundred  is 
united  with  the  1  ten.  1  hundred  is  equal  to  10  tens.  10  tens  and 
1  ten  are  11  tens.  3  tens  from  11  tens  leave  8  tens.  The  8  is  writ- 
ten in  tens'  place. 

Because  5  hundreds  can  not  be  subtracted  from  3  hundreds, 
1  thousand  is  united  with  the  3  hundreds.  1  thousand  equals  10 
hundreds.  10  hundreds  and  3  hundreds  equal  13  hundreds.  5  hun- 
dreds from  13  hundreds  leave  8  hundreds.  The  8  is  expressed  in 
hundreds'  place. 

Since  1  thousand  was  added  with  the  hundreds,  there  are  but 
6  thousands  left.  2  thousands  from  6  thousands  leave  4  thousands. 
The  4  is  written  in  thousand's  place  in  the  remainder. 

Hence  the  remainder  is 


Slate  Exercises. 
Copy  and  subtract  the  following : 


(2.) 

(3.)  • 

(4.) 

(5.) 

(6.) 

6825 

8541 

3412 

1694 

3728 

4376 

7285 

1589 

469 

1963 

I 


IN    ARITHMETIC.  121 

Copy  and  subtract  the  following : 

(7.)  (8.)  (9.)         (10.)  (11.) 

4328  6351  4211  6253  4101 

2579  5472  3587  4897  2853 

12.  A  paid  8,728  dollars  for  his  farm,  and  B  paid 
5,935  dollars  for  his.  How  much  more  did  A^s  farm 
cost  than  B\s? 

13.  There  were  manufactured  in  a  cotton  factory 
1,857  yards  on  Monday,  and  2,139  yards  on  Tuesday. 
How  many  yards  more  were  manufactured  on  Tues- 
day than  on  Monday  ? 

14.  A  man  who  owned  8,754  acres  of  land,  sold 
3,215  acres  to  one  company,  and  2,154  acres  to  an- 
other.    How  many  acres  were  unsold? 

15.  From  eight  thousand,  five  hundred  sixteen, 
subtract  three  thousand,  six  hundred  twenty-four. 

16.  A  mill  was  purchased  for  13,850  dollars,  and 
afterward  sold  at  a  loss  of  2,175  dollars.  How  much 
was  received  for  it? 

Copy  and  subtract  the  following: 

(17.)        (18.)         (19.)        (20.)  (21.) 

15,862   14,684   28,465   35,469  99,846 

9,839   13,299   13,984   24,983  31,985 

(22.)  (23.)  (24.)  (25.)  (26.) 

85,724  27,869  35,321  73,814  125,269 

46,689  13,780  15,094  15,209  48,736 
li 


122 


FIRST    LESSONS 


MULTIPLICATION 


--^- 


LESSON    I.XXII. 

1.  What  will  9  sheep  cost  at  6  dollars  a  head  ? 

2.  What  will  10  quarts  of  milk  cost  at  6  cents  a 
quart  ? 

3.  What  will  be  the  cost  of  4  wagons  at  30  dol- 
lars apiece? 

4.  Since    12   inches    make    one    foot,   how    many 
inches  are  there  in  3  feet? 

5.  At  11  cents  a  quart,  what  will  9  quarts  of  ber- 
ries cost? 

6.  If  a  laborer  can  work  but  13  days  per  month, 
how  many  days  can  he  work  in  3  months? 

7.  In  one   week  there   are   7  days.     How  many 
days  are  there  in  12  weeks? 

8.  If  one  hogshead  of  sugar  is  worth  40  dollars, 
what  are  2  hogsheads  of  sugar  worth  ? 

9.  If  one  apple-tree  yields  14  bushels  of  apples, 
how  many  bushels  will  2  such  trees  yield? 

10.  If  a  man   plants   20  apple-trees   in   one    row, 
how  many  trees  will  he  plant  in  5  such  rows? 

11.  When  loaf-sugar  is  worth   15  cents   a   pound, 
how  much  will  4  pounds  cost? 

12.  What  will  9  dozen  of  peaches  cost  at  10  cents 
per  dozen? 


I 


IN    ARITHMETIC.  12»3 

13.  What  will  be  the  cost  of  3  copy-books  at  20 
cents  each? 

14.  What  will  be  the  cost  of  4  yards  of  muslin  at 
30  cents  a  yard  ? 

15.  If  you  give  25  cents  to  each  of  3  beggars, 
how  much  will  you  give  them? 

DEFINITIONS. 

The  process  of  taking  one  number  as  many  times  as 
there  are  units  in  another,  is  called  Jlultiplication, 

The  number  to  be  taken  or  multiplied  is  called  the 
Mu  ltix>  Ilea  iid. 

The  number  which  shows  how  many  times  the 
multiplicand  is  taken  is  called  the  3£ultiplie7\ 

The  result  obtained  by  multiplying  is  called  the 
JProduct. 

The  Sign  of  Multiplication  is  an  oblique 
cross :  X .     It  is  read  times  or  multiplied  by, 

1.  Multiply  421  by  3. 

■  PROCESS.  Explanation. — For  convenience  the 

i  ct  1  multiplier  is  written  under  the  multipli- 

Multiplicand       421  jr.--         ...       -ixi-ji 

cand.     Beginning  at  the  right  hand  each 

Multiplier      3^  figure  of  the  multiplicand  is  multiplied 

Product  12  6  3  ^y  t^^e  multiplier. 

Thus  3  times  1  unit  are  3  units.  The 
3  is  written  in  units'  place  in  the  product.  3  times  2  tens  are  6  tens. 
The  6  is  written  in  tens'  place  in  the  product. 

3  times  4  hundreds  are  12  hundreds,  which  equal  1  thousand  and 
2  hundreds.  The  1  thousand  is  written  in  thousands'  place  and  the 
the  2  hundreds  in  hundreds'  place  in  the  product. 

Hence  the  product  is  1263. 


124  first  lessons 

Slate  Exercises. 

Copy  and  multiply  the  following : 

(2.)  (3.)  (4.)  (5.) 

6102  5233  5212  7342 

4  3  3  2 


(7.)  (8.)  (9.) 

5234  3123  4123 

2  3  3 


liESSOX    I.XXIII 


1.  How  many  are  8  times  196? 

PROCESS.  Explanation. — For  convenience  the  mul- 
1  Q  ^                tiplier  is  written  under  the  multiplicand.    Be- 
ginning at  the  right  each  figure  of  the  multi- 
^              plicand  is  multiplied  by  the  multiplier. 


;[  5  g  g  Thus,  8  times  6  units  are  48  units.    48  units 

are  equal  to  4  tens  and  8  units.   The  8  is  written 

in  units'  place  in  the  product,  and  the  4  is  reserved  to  add  with  the  tens. 

8  times  9  tens  are  72  tens,  plus  the  4  tens  reserved,  are  76  tens. 
76  tens  are  equal  to  7  hundreds  and  6  tens.  The  6  is  written  in  tens' 
place  in  the  product,  and  the  7  is  reserved  to  add  with  the  hun- 
dreds. 

8  times  1  hundred  are  8  hundreds,  plus  7  hundreds  reserved, 
are  15  hundreds.  15  hundreds  are  equal  to  1  thousand  and  5 
hundreds,  which  are  written  in  hundreds'  and  thousands'  places  in 
the  product. 

Hence  the  product  is  1568. 

The  accuracy  of  the  work  may  be  tested  by  reviewing  it. 


IN     ARITHMETIC.  125 


Copy  and 

multiply : 

(2.) 

(3.) 

(4.) 

(5.) 

1345 

3824 

6325 

7863 

6 

7 
(7.) 

4 

(8.) 

5 

(6.) 

(9.) 

7581 

6274 

6235 

7341 

3 

9 

8 

2 

10.  If  a   ship   sails   368   miles   in   one  week,  how 
many  miles  will  she  sail  in  7  weeks? 

11.  There   are   5280   feet   in   a   mile.     How  many 
feet  are  there  in  9  miles? 

12.  What  will  6  yoke  of  cattle  cost  at  184  dollars 
a  yoke? 

13.  If  1  horse  is  valued  at  275  dollars,  what  is  the 
value  of  6  such  horses? 

14.  If  a  ship  sails  895  miles  in   1  week,  how  far 
will  she  sail  in  9  weeks? 

15.  What  is  the  product  of  457  multiplied  by  7? 

16.  What  is  the  product  of  784  multiplied  by  4? 

17.  If  a  clerk   receives  a  salary  of  972  dollars  a 
year,  how  much  will  he  receive  in  5  years? 

18.  Since  there  are  365  days  in  1  year,  how  many 
days  are  there  in  9  years? 

19.  Multiply  3452  by  3.     Multiply  1472  by  5. 

20.  Multiply  6841  by  6.     Multiply  5261  by  7. 

21.  Multiply  7186  by  3.     Multiply  9167  by  8. 

22.  Multiply  2041  by  8.     Multiply  9380  by  9. 


126  FIRST    LESSONS, 

23.  Multiply  4926  by  6.     Multiply  4829  by  7. 

24.  Multiply  3624  by  4.     Multiply  1684  by  2. 

25.  If  it  takes  5428  shingles  for  the  roof  of  a  house, 
how  many  shingles  will  it  take  for  5  such  houses? 


Copy  and  multiply : 
(26.)     (27.) 
4753     6529 
5       3 

(28.) 

8881 

6 

(29.) 
9573 
4 

(30.) 
2469 

8 

(31.) 

6382 

6 

(32.) 
4629 

7 

(33.) 

3265 

9 

(34.) 

8475 
8 

(35.) 

8463 

4 

3^#^C 


liESSON^   I.XXIV. 
1.  Multiply  435  by  37. 

FIRST  PROCESS.  EXPLANATION. — The  numbers  are 

written  as  before.     Since  in  multiply- 

"^^^         ing  we   multiply  by  the  parts  of  a 

3  7         number,  to  multiply  by  87  we  multi' 


7v425=     2975       ^^^  ^^  ^^  ^"^  ^^  ^'  ^"^  ^^^  ^^^  ^^' 
30X425  --^12750  7  ^j^^^g  425  ^re  2975,  the  first  par- 

37X425=:15725        tial  product ;  30  or  3  tens  times  425 

are  1275  tens  or  12750,  the  second 
partial  product.  The  sum  of  these  partial  products  will  be  the 
entire  product. 

Hence  the  entire  product  is  15725. 


IN    ARITHMETIC.  127 


SECOND  PROCESS.  EXPLANATION. — In  this  process  the 

cipher  at  the  right  of  the  partial  prod- 

^  uct  is  omitted  and  the  significant  figures 

3  7  placed  in  their  proper  places.    Thus,  in 

7y42.5=     2975  multiplying  by  3  lois,  the  product  is 

_               ^'  1275  tens  or  12  thousands  7  hundreds 

o  A  4  -^  0        L  Z  i  0  ^^^  g  j.gj^g^  which  are  written  in  their 

15  7  25  proper  places  in  the  partial  product. 

In  multiplying  by  tens  the  lowest  denomination  of 
the  product  is  tens,  in  multiplying  by  hundreds  it  is 
hundreds,  by  thousands  it  is  thousands.     Hence, 

The  first  figure  of  each  product  should  he  placed 
under  the  figui^e  by  which  we  multiply. 

Slate  Exercises. 


(2.) 
Multiply  3468 
By                12 

(3.) 

4126 

31 

(4.) 

7824 
23 

(5.) 

6846 

43 

(6.) 

7125 

37 

(7.) 
Multiply  4685 
By                76 

(8.) 

7235 

83 

(9.) 

4986 

49 

(10.) 

5843 

121 

(11.) 

1987 

316 

(12.) 
Multiply  5964 
By                73 

(13.) 

6842 

39 

(14.) 

2723 

64 

(15.) 

8962 

135 

(16.) 

8462 

216 

(17.) 
Multiply  8964 
By                 62 

(18.) 

3562 

36 

(19.) 

7825 

47 

(20.) 

3265 

234 

(21.) 

9268 

327 

128 


FIRST    LESSONS 


uMMm 


D  I  V  I   S  I  O  N 


tzz=i 


1.  How  many  barrels  of  flour  at  8  dollars  a  barrel, 
can  be  bought  for  72  dollars? 

2.  If  there  are  3  feet  in  a  yard,  how  many  yards 
are  there  in  27  feet? 

3.  At  4  dollars  a  cord,  how  many  cords  of  wood 
can  be  bought  for  40  dollars? 

4.  If  a  man  can  walk  4  miles  per  hour,  how  long 
will  it  take  him  to  walk  36  miles? 

5.  If  5  paces  are  a  rod  of  distance,  what  is  the 
length  in  rods  of  a  piece  of  land  which  is  30  paces 
long  ? 

6.  If  paper  is  put  in  packages  containing  6  sheets 
each,  how  many  packages  can  be  made  out  of  48 
sheets  ? 

7.  If  5  bushels  of  wheat  make  a  barrel  of  flour, 
how  many  barrels  of  flour  can  be  made  from  40 
bushels  of  wheat? 

8.  At  6  dollars  a  ton,  how  many  tons  of  hay  can 
be  bought  for  54  dollars? 

9.  If  a  man  can  build  7  rods  of  fence  in  one  day, 
in  how  many  days  can  he  build  35  rods? 

10.  If  a  teacher  earns  9  dollars  a  week,  in  how 
many  weeks  can  she  earn  90  dollars?  . 


IN    ARITHMETIC.  129 

DEFINITIONS. 

The  process  of  finding  how  many  times  one  num- 
ber is  contained  in  another  is  called  JDivision, 

The  number  to  be  divided  is  called  the  Divi- 
dend. 

The  number  by  which  the  dividend  is  to  be  di- 
vided is  called  the  Divisor. 

The  result  in  division  is  called  the  Quotient, 

The  part  of  the  dividend  remaining  when  the  di- 
vision is  not  exact  is  called  the  Remainder, 

The  Sign  of  Division  is  -f-,  read  divided  by. 

Til  us,  24  -f-  6  is  read,  24  divided  by  6. 

1.  How  many  times  is  3  contained  in  369? 

FIRST  PROCESS.  EXPLANATION.  —  For    Convenience 

Divisor.  Dividend.  Quotient.        the  divisor  is  written  at  the  left  of  the 
3)36  9(100  dividend,  and  the  quotient  at  the  right. 

Beginning  at  the  left  we  divide. 

3  is  contained  in  369    I    hundred 
times   and   a  remainder.     The   100   is 
placed  in  the  quotient,  and  the  divisor 
is  multiplied  by  it.     The  product  300 
is  written   under   the  dividend.     Sub- 
tracting there  is  a  remainder  of  69. 
3  is  contained   in  69,  20  times  and  a  remainder.     The   20  is 
placed   in    the   quotient    and    the   divisor   multiplied  by  it.     The 
product  60  is  written  under  the  partial  dividend.     Subtracting  the 
remainder  is  9. 

3  is  contained  in  9,  3  times  and  no  remainder.    The  3  is  placed  in 
the  quotient,  and  the  divisor  multiplied  by  it.     The  product  9  is  writ- 
ten under  the  partial  dividend.     Subtracting,  there  is  no  remainder. 
The  true  quotient  is  therefore  the  sum  of  the  partial  quotients, 
which  is  123,  and  3  is  contained  in  369,  123  times. 


300 

20 

69 

3 

60 

123 

9 

9 

130  FIRST     LESSONS 

SECOND  PROCESS.  EXPLANATION. — The  second  process  is 

•§  g  i  the  same  as  the  first,  except  that  the  ciphers 

QNQAQ/'IOQ  ^^^  omitted  from  the  right  of  the  quotient 

o)oov[iAo  figures  and  partial  products,  the  value  of 

^ figures  being  indicated    by   their  position. 

g  Thus,  the  figures  of  the  quotient  are  1  hun- 

Q  dred,  2  tens,  and  3  units,  which  are  written 

— — '  in  succession  so  that  each  figure  represents 

"  its  proper  value. 

^  The  products  3  hundreds,  6  tens  and  9 

units  are  placed  under  hundreds,  tens,  and 
units  in  the  partial  dividends. 

Slate  Exercises. 
Copy  and  divide  the  following : 

(2.)  (3.)  (4.)  (5.) 

4)488(        5)550(        3)699(        2)264( 


liESSOI^   I.XXVI. 

1.  How  many  times  is  6  contained  in  1398  ? 

PROCESS.  Explanation. — For  convenience  the  di- 

fi^l  ^98^2*^'^  visor  is  written  at  the  left  of  the  dividend 

-I  9  and  the  quotient  at  the  right.      Beginning 

at  the  left  of  the  dividend  we  divide. 

1  «^  6  is  not  contained  in  1   thousand  any 

1  8  thousand  times,  therefore  the  quotient  can 

2  g  not  be  higher  than  hundreds.      Hence  we 

-I  Q  must  find  how  many  times  6  is  contained 

in  all  the  hundreds  of  the  dividend. 

1  thousand  is  equal  to  10  hundreds.    10 
hundreds  plus  3  hundreds  equal  13  hundreds.     6  is  contained  in 


IN    ARITHMETIC, 


131 


13  hundreds  2  hundred  times  and  a  remainder.  The  2  is  written 
in  hundreds'  place  in  the  quotient  and  the  divisor  multiplied  by  it. 
Subtracting  this  product  from  the  partial  dividend,  13  hundreds, 
there  is  a  remainder  of  1  hundred. 

1  hundred  remainder  is  equal  to  10  tens.  10  tens  plus  9  tens 
equal  19  tens.  6  is  contained  in  19  tens  3  tens  times  and  a  re- 
mainder. The  3  is  written  in  tens'  place  in  the  quotient,  and  the 
divisor  multiplied  by  it.  Subtracting  this  product  from  the  partial 
dividend,  19  tens,  there  is  a  remainder  of  1  ten  in  the  quotient. 

The  1  ten  remainder  equals  10  units.  10  units  plus  8  units 
equal  18  units.  6  is  contained  in  18  units  3  times  and  no  re- 
mainder. The  3  is  written  in  units'  place  in  the  quotient,  and  the 
divisor  multiplied  by  it. 

Hence  the  quotient  is  233. 


Slate  Exeecises. 
Copy  and  divide  the  following: 

(2.)  (3.)  (4.) 

5)32860(       8)72880(       6)63546( 


(6.) 
4) 87564 ( 

(10.) 
6) 38412 ( 


(7.) 
7) 67326  ( 

(11.) 
5)  42865 ( 


(8.) 
9) 27819  ( 

(12.) 
8) 32848  ( 


(5.) 
3) 56841  ( 

(9.) 
7) 58562 ( 

(13.) 
4) 48264  ( 


(14.)  (15.)  (16.)  (17.) 

7) 54285 (       9) 32616 (       8) 42856 (       9) 49842  ( 

The  solution  of  examples  having  a  small  divisor, 
may  be  shortened  by  performing  the  multiplications 
and  subtractions  without  waiting  the  results.  This 
process  is  called  Short  Division. 


132 


FIRST    LESSONS 


PROCESS. 

6)1398 
233 


The  solution  of  Example  1,  by  short  division,  is: 

Explanation. — 6  is  contained  in  13  hun- 
dreds 2  hundred  times  and  1  hundred  remain- 
der. The  2  is  written  in  the  quotient  under 
units  of  the  same  order  in  the  dividend. 

1  hundred  remainder  and  9  tens  make  19 
tens.  6  is  contained  in  19  tens  3  tens  times  and  1  ten  remainder.  The 
3  is  written  in  the  quotient  under  tens  in  the  dividend. 

1  ten  remainder  and  8  units  make  1<S  units.    6  is  contained  in 
18  units  3  times.    The  3   is  written  in  the  quotient  under  units. 
Hence  the  quotient  is  233. 


Solve  by  short  divisio 

Q  : 

18.  4761  -^  3. 

37. 

6435^5. 

19.  5848-^4. 

38. 

3280  -4-  8. 

20.  3725 -f- 5. 

39. 

3689-4-7. 

21.  4865-^7. 

40. 

8262^9. 

22.  2844-^6. 

41. 

5984  ^  4. 

23.  7254^9. 

42. 

6975-^5. 

24.  9328 -f- 8. 

43. 

4284^7. 

25.  6832-^7. 

44. 

6720-^8 

26.  9745-^5. 

45. 

9873  -^  9. 

27.  6835-^5. 

46. 

3248-^8. 

28.  7281  -^  9. 

47. 

5274  -^  6. 

29.  3234-^6. 

48. 

8245  ^  5. 

30.  5948 -f- 4. 

49. 

3824  ^  4 

31.  4275-^3. 

50. 

4920-4-8 

32.  3577 -f- 7. 

51. 

3915^9 

33.  3486-4-6. 

52. 

4823  -4-  7 

34.  9648^8. 

53. 

4625-4-5 

35.  8936^9. 

54. 

9441  ^  3. 

36.  8532^6. 

55. 

8928  -4-  6. 

IN    ARITHMETIC. 


133 


liESSON    LiXXVII. 


1.  Divide  4825  by  26. 


PROCESS, 
pivisor.  Dividend.  Quotient 

26)4825(185 
26 


222 
208 


145 
130 


Explanation.— 26  is  not  contained 
in  4  thousands  any  thousands  times, 
hence,  the  thousands  are  united  with 
the  hundreds,  making  48  hundreds.  26 
is  contained  in  48  hundreds  1  hundred 
times  and  a  remainder.  The  1  is  writ- 
ten in  hundreds'  place  in  the  quotient 
and  the  divisor  multiplied  by  it,  giving 
a  product  of  26  hundreds.  Subtracting 
this  product  from  the  partial  dividend 
48,  there  is  a  remainder  of  22  hundreds. 
22  hundreds  united  with  2  tens 
make  222  tens.  26  is  contained  in  222  tens  8  tens  times  and  a  re- 
mainder. The  8  is  written  in  tens'  place  in  the  quotient  and  the 
divisor  multiplied  by  it,  giving  a  product  of  208  tens.  Subtracting 
this  product  from  the  partial  dividend  there  is  a  remainder  of  14  tens. 
14  tens  united  with  5  units  make  145  units.  26  is  contained  in 
145  units  5  times  and  a  remainder.  The  5  is  written  in  units'  place 
in  the  quotient  and  the  divisor  multiplied  by  it,  giving  a  product  of 
130  units.     Subtracting,  there  is  a  remainder  of  15. 

Therefore  the  quotient  is  185,  and  the  remainder,  15. 


Remainder      1  5 


Divide : 

Divide : 

2.  864  by  12. 

10. 

3358  by  73 

3.  845  by  13. 

11. 

4788  by  84 

4.  906  by  21. 

12. 

3696  by  66 

5.  1188  by  22. 

13. 

1904  by  28 

6.  2016  by  32. 

14. 

3277  by  29 

7.  1486  by  33. 

15. 

5706  by  46 

8.  2016  by  30. 

16. 

45658  by  37 

9.  2397  by  51. 

17. 

55484  by  26 

134  FIRST    LESSONS 


liESSOX    I.XXTIII. 
UNITED  STATES  MONEY. 

The  money  of  the  United  States  is  called  United 
States  Money, 

The  standard  unit  is  the  dollar, 

TABLE. 

10  Mills  are  equal  to   1  Cent. 
10  Cents     "         "        "   1   Dime. 
10  Dimes  "        "       "    1  Dollar. 

The  denomination  dimes  is  not  generally  used. 

The  Sign  of  Dollars  is  %,  a  supposed  combination  of  U.  S. 

1.  How  many  mills  are  there  in  2  cents?  In  5 
cents  ?     In  10  cents  ? 

2.  How  many  cents  are  there  in  2  dimes  ?  In  4 
dimes?  In  7  dimes?  In  10  dimes  or  1  dollar?  In 
5  dimes  or  one-half  of  a  dollar  ? 

3.  How  many  cents  are  there  in  |2  ?  In  $3  ?  In 
$4?     In  $5? 

4.  How  many  dollars  are  there  in  200  cents?  In 
300  cents?     In  400  cents?     In  500  cents? 

5.  In  450  cents  how  many  dollars  are  there,  and 
how  many  cents  besides?  In  375  cents?  In  425 
cents  ?     In  870  cents  ?     In  684  cents  ?     In  296  cents  ? 


IN    ARITHMETIC. 


135 


1.  In  expressing  dollars  and  cents  by  figures,  a  period  called  the 
decimal  point,  is  placed  between  the  dollars  and  the  cents.  Thus, 
265  cents  are  equal  to  $2.65,  which  is  read,  2  dollars,  65  cents. 

2.  When  less  than  10  cents  are  written,  a  cipher  must  be  written 
before  the  number.     Thus,  5  cents  are  written,  $.05. 

3.  Mills  are  written  after  the  cents.  Thus,  $2,655  is  read,  2 
dollars,  65  cents,  5  mills. 

6.  Read  the  following: 

$3.25;    $6.38;    $7.24;    $6.05;    $2.46;    $7.24; 
$5.18;    $7.36;    $3.02;    $5.07;    $2.15;    $4.16. 

7.  Write  the  following  : 

Five  dollars   twenty-nine  cents. 
Seven  dollars   sixty-eight  cents. 
Eight  dollars   seventy-seven  cents. 
Forty-eight  dollars  sixteen  cents. 
Thirty-four  dollars    nine  cents. 
Sixty-eight  dollars   nineteen  cents. 


3^^C 


liESSOX    I.XXIX 
Slate  Exekcises. 
Copy  and  add  the  following : 
(1.)  (2.)  (3.) 

$63.28  $32.18  $24.16 
47.15  25.16  37.18 
21.15         17.24         22.39 


(4.) 

(5.) 

$38.24 

$29.66 

29.16 

18.39 

45.77 

14.27 

136 


FIEST    LESSONS 


Copy  and  subtract  the  following: 

(6.)           (7.)           (8.)           (9.)  (10.) 

$69.84      $63.18       |36.27       $17.64  $33.64 

21.39         24.24         28.39           8.89  17.25 


(11.)         (12.)  (13.)  (14.)  (15.) 

$16.00      $45.10      $46.00       $28.76       $64.35 

13.28         33.49         25.18         18.87         57.47 

Arrange  in  columns  and  add  : 

16.  $12.27,  $15.34,  $18.29,  $64.38,  $15.92,  $2.68. 


17.  $8.37,    $28.05,  $36, 

18.  $5.06,-  $2.18,  $.34, 

19.  $3.25,    $4.26,  $8.35, 

20.  $8.29,    $4.34,  $5.69, 

21.  $14.24,  $8,  $3.46, 


$14.29,  $25,  $1.25. 

$.08,       $5.22,  $18. 

$13,        $15.92,  $14.96. 

$8.34,     $7.29,  $6.84. 

$.75,       $2.84,  $7.50. 


How  many  are 

How  many  are 

22.  3     times  $18.24? 

28.  18  times  $16.24? 

23.  7     times  $21.36? 

29.  30  times  $45.61? 

24.  12  times  $34.29? 

30.  24  times  $8.64? 

25.  15  times  $34.09? 

31.  35  times  $16.80? 

26.  5     times  $19.26? 

32.  32  times  $18.25? 

27.  8     times  $34.18? 

33.  25  times  $15.24? 

What  is 

What  is 

34.  ^  of  $24.35? 

38.    i    of  $38.43? 

35.  i  of  $13.30? 

39.  -jV  of  $34.24? 

36.  i  of  $24.36  ? 

40.  j\  of  $9.40? 

37.  I  of  $32.48? 

41.  -^  of  $74.26? 

IN    ARITHMETIC.  137 

IjESSON    liXXX. 

MEASURES  OF  LENGTH. 

The  measures  used  in  determining  length,  or  the  dis- 
tance of  one  place  from  another,  are  called  Measures 
of  Length. 

TABLE. 


12  Inches  are 

equal  to  1  Foot. 

3  Feet 

"      "  1  Yard. 

b\  Yards')    « 
16^  Feet     i 

"      "  1  Rod. 

320  Rods 

"      "  1  Mile. 

1.  How  many  inches  are  there  in  2  feet?  In  3 
feet  ?     In  5  feet  ?     In  i  of  a  foot  ?     In  J  of  a  foot  ? 

2.  How  many  feet  are  there  in  24  inches?  In  36 
inches?    In  48  inches?    In  60  inches?    In  72  inches? 

3.  How  many  feet  are  there  in  3  yards?  In  4 
yards?     In  8  yards?     In  9  yards? 

4.  How  many  inches  are  there  in  1  yard?  In  2 
yards?     In  4  yards? 

5.  How  many  feet  are  there  in  2  rods?  In  2  rods 
and  5  feet  ?  In  2  rods  and  10  feet  ?  In  2  rods  and 
2  yards? 

6.  How  many  rods  are  there  in  2  miles  ?  In  3 
miles?     In  5  miles? 

7.  This  line  is  1  inch  long  I  i  I  ■  I  ■  I  ■  I.  Cut 
a  string  a  foot  in  length.  A  yard  in  length.  A  rod 
in  length. 

8.  Name  two  places  a  mile  apart.     Two  miles. 

12 


FIRST    LESSONS 


r.Esso:Nr  i^xxxi 

LIQUID  MEASURES. 


The  measures  used  in  measuring  all  kinds  of  liquids 
are  called  Liquid  Measures, 


TABLE. 

4  Gills  are  equal  to  1  Pint. 
2  Pints    "        "      "  1  Quart. 
4  Quarts "         "      "  1  Gallon. 

In  estimating  the  capacity  of  cisterns,  reservoirs,  etc.,  31 J  gallons 
are  considered  a  barrel,  and  63  gallons  a  hogshead. 

1.  Name  some  articles  that  are  bought  and  sold 
by  the  gallon,  quart,  pint,  or  gill. 

2.  How  many  gills  are  there  in  2  pints?     In  3 
pints?     In  5  pints?     In  10  pints?     In  12  pints? 

3.  How   many  pints  are  there   in   5   quarts?     In 

7  quarts?     6  quarts?     8  quarts? 

4.  How  many  quarts  are  there  in  5  gallons  ?     In 

8  gallons?     7  gallons?     6  gallons? 

5.  How   many   pints  are  there   in    12    gills?     In 
16  gills?     In  15  gills?     In  21    gills?     In   32  gills? 

6.  How  many    gallons   are  there   in    12    quarts? 
In  16  quarts?     In  15  quarts?     In  25  quarts? 


IN    ARITHMETIC. 


139 


LESSOR    I.XXXII. 

DRY  MEASURES. 

The    measures    used    in     measuring    grain,    roots, 
fruit,  etc.,  are  called  Ury  Measures. 

TABLE. 

2  Pints  are  equal  to  1  Quart. 
8  Quarts  "  "  "  1  Peck. 
4  Pecks    "        "       "    1  Bushel. 

In  measuring  coarse  commodities  the  measure  should  be  heaped. 
In  measuring  grain,  seeds,  etc.,  the  measure  should  be  even  full. 

1.  Name  some  articles  that  are  bought  and  sold 
by  the  bushel,  peck,  or  quart? 

2.  How   many   pints   are  there  in  4  quarts?     In 
8  quarts?     In  2   pecks?     In  3  pecks?     In  4  pecks? 

3.  How    many    pecks    are   there    in    2    bushels? 
In  5  bushels?     In  8  bushels?     In  10  bushels? 

4.  How    many    quarts    are    there    in    40    pints? 
In  60  pints? 

5.  How    many  bushels   are   there    in    32    pecks? 
In  40  pecks? 

6.  What  will  2  pecks  of  berries  cost  at  3  cents 
a  pint? 


140  FIRST    LESSONS 

LESSOR    I.XXXIII. 

MEASURES  OF  WEIGHT. 

The  weights  used  in  measuring  all  coarse  and  heavy 

articles,  as  hay,  grain,  gro- 
ceries, coal,  flour,  etc.,  and 
all  the  metals  except  gold 
and  silver,  and  all  drugs 
except  medicines  com- 
pounded in  prescriptions, 
are  called  Avoirdupois  Weights. 

TABLE. 

16  Ounces  are  equal  to  1  Pound. 
100  Pounds    "        "       "   1  Hundred-weight. 
20  Hundred- weight      "   1  Ton. 

1.  How    many    ounces   are    there    in    3    piounds? 
In  5  pounds? 

2.  How  many    pounds  are  there  in    7    hundred- 
weight?    In  9  hundred-weight? 

3.  How   many    pounds  are  there    in  1    ton?     In 
2  tons?     In  5  tons? 

4.  How  many  tons  are  there  in  6000  pounds? 

5.  How     many     tons    and    hundred-weight    are 
there  in  4500  pounds?     In  2900  pounds? 

6.  How  many  tons,  hundred-weight,  and  pounds 
are  there  in  4625  pounds?     In  2643  pounds? 

7.  What  will  6  hundred-weight  of  sugar  cost  at 
9  cents  per  pound  ?     At  10  cents  per  pound? 


I 


IN    ARITHMETIC. 


141 


8.  If  a  bushel  of  wheat  weighs  60  pounds,  how 
many  bags  that  hold  2  bushels  each  will  be  required 
to  hold  4800  pounds? 

9.  What  will  5  pounds  of  indigo  cost  at  5  cents 
an  ounce?     What  will  7  pounds  cost? 

liESSOX    I^XXXIT. 

MEASURES  OF  TIME. 

The  names  of  the  ordinary  divisions  of  time  are 
seconds,  minutes,  hours,  days,  weeks,  months,  and  years. 


TABLE. 

60  Seconds 

are 

equal 

to  1  Minute. 

60  Minutes 

iC 

(C 

"   1  Hour. 

24  Hours 

(I 

u 

"   1  Day. 

7  Days 

l( 

u 

"   1  Week. 

30  Days 

u 

u 

"   1  Month. 

12  Months 

a 

It 

"   1  Year. 

365  Days 

it 

It 

"   1  Year. 

100  Years 

i( 

ti 

"   1  Century 

1.  How  many  seconds   are    there  in   5  minutes? 
In   6   minutes?     In   10  minutes? 

2.  How  many  minutes  are  there  in   2  hours? 
J  of  an   hour?     In   i   of  an   hour? 

3.  How  many  hours   are   there   in 
}  of  a  day?     In  J  of  a  day?     In  \ 

4.  How  many  days  are   there   in   4  weeks? 
6  weeks?     In   7   weeks?     In   10  weeks? 


2  days? 
of  a  day? 


In 


In 


In 


142 


FIRST    LESSONS 


5.  What   part   of  an    hour  are  30   minutes?     15 
minutes?     45   minutes? 

6.  How    many    hours    are    there    in    90   minutes? 
In  120   minutes?     In   180   minutes? 

7.  How  many  centuries  are  there  in  1500  years? 

8.  Of  what  century  is  the  year  1501   a  part? 

TABLE  OF  MONTHS. 


Oi-der. 

Name. 

No.  of  Days. 

Season. 

Ist. 
2d. 
3d. 

January, 

February, 

March, 

31. 

28  or 
31. 

29. 

1  Winter. 

4th. 
5th. 
6th. 

April, 

May, 

June, 

30. 
31. 
30. 

V  Spring. 

7th. 
8th. 
9th. 
10th. 

July, 

August, 

September, 

October, 

31. 
31. 

30. 
31. 

Summei 
\  Autumr 

11th. 

November, 

30. 

i 

12th. 

December, 

31. 

1  Winter. 

365 


\m. 


1. 

2. 
4th? 


RHYME  OF  THE  MONTHS. 

Thirty  days  hath  September, 

April,  June,  and  November. 

All  the  rest  have  thirty-one 

Save  February,  which  alone 

Hath  twenty-eight,  and  one  day  more 

We  add  to  it  one  year  in  four. 

Kepcat  the   months  in  their  order. 
What    is    the    5th    month?      The    7th? 
The  3d?     The   10th?     The   8th? 


The 


IN    ARITHMETIC.  143 

3.  What  are  the  months  of  Winter?     Summer? 
Spring?     Autumn? 

4.  How    many    months    have     30    days?      How 
many  31  days? 

COUNTING. 

The  following  denominations  are  used  in   count- 
ing some  classes  of  articles : 

TABLE. 

12  things  are  called  1  dozen. 

12  dozen  "         "  1  gross. 

12  gross  "        "  1  great  gross. 

20  things  "        "  1  score. 

1.  How  many  eggs  are  there   in   6  dozen  eggs? 

2.  How  many  dozen  are  there  in   2  great  gross? 

3.  How  many  are  J  dozen  dozens  of  eggs? 

4.  How  old  is  a    man   who   is  3  score  years  of 
age?     3  score  and  10? 

STATIONERS'  TABLE. 
The  denominations  used    in  the  paper  trade  are : 

*■    24  sheets  are  equal  to  1   qnire. 
20  quires    "         "       **    1  ream. 

1.  How    many    sheets    of  paper   are    there    in    2 
quires  ?     In  J   of  a  quire  ?     In   J   of  a   quire  ? 

2.  How  many  quires  are  there   in  2   reams?     In 
i  of  a  ream  ?     In  J  of  a  ream  ? 

3.  What    will    be    the    cost   of  a   ream    of  paper 
at  20  cents  a  quire  ?     At  1  cent  a  sheet  ? 


144 


FIEST     LESSONS 


1.  The  method  of  expressing  numbers  by  letters 
is  called  the  Homan  Notation, 

Letters.     I,      V,      X,      L,      C,      D,      M. 

Values.     1,        5,      10,     50,    100,  500,  1000. 

TABLE  OF  KOMAN  NOTATION. 


I 

....     1 

XXII 

.    .    .    22 

II 

....      2 

XXIII 

XXIV 

.     .     .    23 

Ill 

....      3 

.    .    .     24 

IV     ....    . 

....      4 

XXV 

.     .     .    25 

V 

....      5 

XXVI 

.     .     .    26 

VI 

....      6 

XXVII      .... 

.     .    .     27 

VII 

....      7 

XXVIII    .... 

.    .     .     28 

VIII      .... 

.    .     .     .      8 

XXIX 

.    .    .    29 

IX 

....      9 

XXX 

.     .     .     30 

X 

....    10 

XL 

.    .    .     40 

XI 

•    •     .    .    11 

L  . 

.    .     .    50 

XII 

....     12 

LX 

.    .    .    60 

XIII      .... 

....     13 

LXX 

.    .     .    70 

XIV 

....     14 

LXXX 

.    .     .    80 

XV 

....     15 

XC 

^    .     .    90 

XVI ....    . 

....     16 

C 

.    .    .100 

XVII     .... 

....    17 

CC 

.    .    .200 

XVIII  .... 

....    18 

CCCC 

.    .    .  400 

XIX 

....    19 

J^,..=:w-     .     . 

.     .     .  500 

XX 

•     •     '^ 

.    .     .  800 

XXI 

.  .  /c^ 

.    .     1000 

o** 


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